What is Yaw?
I have made this very simple so the average Joe can understand what the industry is offering and all of the FTP LT techies can nitpick it apart and tell you what I am missing. Also make sure your calculator is in degrees and not radians!
Each aero test on the market you see how the wheels, bike, helmet compare in 0-20 degrees yaw, but what does this mean to me?
The angle of yaw is simply the amount of crosswind on your bike. Below is a simple graphic to help calculate the yaw angle that you see when you ride.
To start out we will assume that all other variables such and leaning into the wind, gusts, gravity, and a billion other variables cancel out. From here the wind direction would be based on a stationary American flag flapping in the wind. If there is a straight head wind is when theta_wind = 0 degrees, a straight crosswind is 90 degrees and a tail wind is when theta_wind = 180 degrees. Since we are looking at how much cross wind there is we will use the sine function:
F_Cross = F_Wind * sin(theta_wind)
Now we must calculate the F_relative. This incorporates the wind speed and velocity of the cyclist. Since the wind speed is relative to the cyclist there is no angle on the cyclist.
F_Relative = F_Bicycle + F_Wind * cos(theta_wind)
At this point we can relatively easily calculate yaw angle since the yaw angle is simply the relative Velocity of crosswind to the cyclist.
tan(theta_yaw) = (F_Cross) / (F_Relative)
theta_yaw = arctangent(F_Cross / F_Relative)
So plugging it all in :
theta_yaw = arctangent[ (F_Wind * sin(theta_wind)) / (F_Bicycle + F_Wind * cos(theta_wind)) ]
What you will quickly notice is that the ratios that the industry uses are quite small. For a rider going 25 mph below is a chart of what the cross winds would need to be to have a 5, 10, 15, 20 degree yaw.
Yes these values are quite small but you need to keep in mind that this is straight crosswind speed. Since this is all just geometry we can plug in velocities instead of forces. If the wind was at 45 degrees cross head wind and you wanted to have 20 degree yaw angle we would be talking 20 mph wind. Now here is where it gets crazier…if you turn around and now the wind is a cross tail wind of 20 mph at 45 degrees you would now have a yaw angle of more than 45 degrees. Why? Your relative velocity (V_relative) is only 10 mph and your V_cross is still 14 mph…in a cross tail wind a 20 degree yaw angle is a mere 9.5 mph at 25 mph!
Zero degrees yaw:
This is simple, a straight head wind, small differences between bikes and wheels.
15-20 degrees yaw:
For those of you that live along a coast or in the midwest this is the important data points. What I do is just look and see what the aero data is doing in this area because this is the closest conditions to which we race.
Defects in yaw:
If you look at the curves it actually looks like drag decreases with yaw. The aero drag decreases but other forces, angles, and body position changes causing increases in other areas…Or I’d be riding my bike sideways!
Just food for thought…
That said…I am YAWning,