Many of our articles mention Yaw but we have never taken the time to explain what Yaw is and how you calculate it. Luckily Jeff (an AeroGeeks reader who is new to the sport) reminded us that not everyone has the a degree in physics and could use a bit of helping in understanding the concept – Thanks Jeff!
There are a number of aerodynamic forces at work on a rider at any given point in time—the speed at which the rider is moving, the bearing of the bike, and the wind speed and angle relative to the rider. Combined, these numbers equate into what can be reasonably easily understood as yaw.
You Mean Those Chart Things?
This is the chart from Felt’s AR launch that we analyzed during Interbike 2013, showing a number of different bikes’ drag values, measured in grams, at a given angle to the wind being generated by the tunnel. A good rule of thumb is that 100g of drag is worth 1 second per kilometer on the bike—about 37 seconds over an Olympic-distance bike course. Lower, then, is decidedly better.
It is worth noting here that a number of companies are converting from grams of drag, the raw measurement in a wind tunnel, to watts for their charts. For our purposes, this doesn’t matter significantly. We’ll just keep in mind that a company has to make some assumptions in order to make the calculations. Raw, when dealing with data, is always better than interpreted. What we’re really interested in, however, are the degrees that make up the x-axis of the graph, which are commonly referred to as “yaw.”
The data from Felt is a -20 to +20 sweep, which means that Felt recorded the drag on their bikes from 20 degrees off the left side of the bike (about 11 o’clock) to 20 degrees on the right side (1 o’clock), and paused every 2.5 degrees to record another data point. If this doesn’t sound like a huge sweep to you, it’s because it isn’t; there’s simply no reason to go out beyond twenty degrees on either side of the bike, due to this being an apparent wind, or yaw, measurement of drag. What does that mean, though? Why is it so shallow? To answer those questions, let’s explain what we mean when we say apparent wind, more commonly referred to as yaw.
Adding it all together
When you calculate yaw, what you’re really calculating is the angle of the sum of the drag forces acting on a rider. The reason it’s just an angle, or as is commonly referred to, a number of degrees from straight ahead, is because the math works from component forces that use a measurement of force in a given set of directions – in our case, directly ahead and from the side only, leaving out lift and downforce, which lets us describe a given angle in a plane without getting into anything really crazy.
To calculate yaw, we need to know three things: our speed on the bike, how fast the wind is blowing, and what angle the wind is coming from. The first one is easy—simply check your cyclocomputer and it’ll tell you how fast you’re moving. The latter measurements, wind speed and direction, are somewhat tougher to gauge accurately. First, you have to be stopped in order to determine wind direction, otherwise the wind you’re generating by riding will shift your perception of the actual wind. Second, wind speed is tricky to measure even at the best of times, but we’ll discuss that later. For the moment, take a look at the Beaufort Scale to get an understanding of what we’re talking about.
Once we have all of those numbers, we can combine them to get a sort of “imaginary wind,” with both an angle and speed, which combines the natural wind and the wind we’re creating by riding into a single wind that encompasses them both. The angle of our imaginary wind is the degree of yaw from the chart above. The speed is how much force we’re being pushed from that direction, and would ideally be close to that of the tunnel, usually 30 mph. (Note: if your yaw wind is anywhere close to 30, you’re either a professional triathlete or regularly ride the Queen K. Either way, we’re jealous.)
Unfortunately, there’s no simple way to do these sorts of calculations without using math you’ve likely forgotten since college… If you ever had a course in it in the first place, which is unlikely if you weren’t an engineering, mathematics, or science student of some form. Nevertheless, we shall do our best to explain it all to you in an easy-to-follow format. But if this isn’t something you’re interested in, feel free to skip it.
Here There Be Math
For simplicity’s sake, we’ll use the engineer’s best friend, Wolfram Alpha, to assist with our calculations. Let’s say we are riding along at a race pace, 25 mph, and have a crosswind of 5 miles per hour – this is a fairly strong crosswind, see our notes about that below – and it’s coming directly across our right shoulder, which makes the angle 45 degrees. The first thing we need to do is break this out into the component forces we discussed earlier, our x and y magnitudes. Remembering our trigonometry, our crosswind speed is the hypotenuse of a right triangle, where the other two sides represent the component forces, and so we can obtain them through the following formulae:
crosswind x = windspeed * cos(45 degrees);
crosswind y = windspeed * sin(45 degrees);
Wolfram Alpha gives us our answers; 3.54 for both x and y components (this method will work for any angle, it just happens that 45 degrees gives identical answers because it is exactly halfway between a true crosswind and a true headwind).
Next, we take our crosswind y component, the bit that makes you slow, and add it to our own wind. Our own wind? Well, yes; we are moving at 25 miles an hour, creating exactly as much air resistance as a headwind of the same speed. So, our final y component is our speed, 25mph, plus our crosswind y component, 3.54, for a total of 28.54. Our final x is identical to our crosswind x, because we aren’t riding sideways, and so our speed has no x component.
What we end up with is a final x of 3.54 and final y of 28.54. Now let’s come back to our triangle—we can take advantage of trigonometry and realize that we have a final triangle that looks like this:
This gives us the speed of our yaw wind, 28.76 miles per hour, but not the angle, which is the yaw we were after in the first place. Thankfully, this is easy enough to calculate, using arcsine, resulting in this equation:
Our final result is 7.07 degrees, and this is our yaw. Note that this is a very small angle, even though the wind itself was coming at us from a relatively large angle of 45 degrees, due to the wind at ground level being a mere 5 miles per hour. Had it been larger, say a significant crosswind of 10 miles an hour, our result jumps a whopping 5.35 degrees, to 12.43! Still well within the testing angles of every yaw sweep you’re likely to see, and for good reason: you’re almost never riding at anything past 10 degrees of yaw.
A Note On Wind Speeds
“Hang on a minute,” we hear you say, “there was a 20 mile an hour crosswind last weekend and I was nearly blown over! You’ve only gone as high as 10!” We have, you’re right, but that’s because your figures are off. Way off. And, for once, you really can blame the government for it. Or, if you’re more inclined to accuracy, you can blame a man by the name of Gustav Hellmann.
The equation for determining wind at a given height (we’ll use one meter) based off of the wind at a different height (the weather report on your phone is at roughly 10 meters) uses something called the Hellmann exponent, which describes the conditions on the ground that affect the wind above it. We bring him up because for most of our riding, we’re in places with a Hellmann exponent of around 0.20-.025, and so our “20 mile an hour” reported speed crosswind ends up having a final crosswind like this:
And our crosswind is a still-stiff 11.25 miles an hour. That’s a far cry from the 20 mph battle we were having just a moment ago, though, and illustrates why the bulk of our riding is done at 0-10 degrees of yaw, with the average being around 7. If you were riding into an actual 20 mph crosswind, you’ve decided to go for a training ride during a tropical storm, and we’d recommend that you find shelter quickly.
We hope this has been a reasonably thorough, and understandable, explanation of yaw. We encourage you to use the Wolfram Alpha links to the equations used in this explanation to play around and see what your own numbers look like – we think you’re likely to be surprised at just how narrow a range you really ride in.