Yaw Drag & Component Choice

"Ignore your aircrafts crosswind limits and yaw'll be sorry" reads a popular safety poster aimed at trainee pilots. This has little to do with cycling but it gives a big clue what yaw is all about - the idea that, in crosswind conditions, the direction of airflow hitting a moving object - such as an aeroplane or a bike - is some combination of the direction of motion and direction of the wind. For the poor trainee pilot this poses certain control challenges, while for the cyclist it has real relevance to drag and equipment choice.

To help in our discussion of yaw, let's define two kinds of wind. There is the wind that blows due to weather, perhaps a south westerly breeze blowing at 10 kph, from now on we'll call it the meteorological wind. And there is the "wind" that we perceive due to cycling at speed, even on a flat-calm day with zero meteorological wind you experience some of this "wind" in your face. Of course this isnt wind in the true sense, rather a cyclist moving through a (still) body of air experiences a sensation the same as if the rider was static and the wind was blowing at the speed of the rider. Many people would refer to this wind as wind resistance and so we'll call it resistance wind.

It follows that in a real word environment a rider experiences some meteorological wind, which has a strength and a bearing you might figure from a weather report, and some resistance wind, depending on the speed he is riding but always with a bearing directly in his face. It also follows that these two winds combine or offset to create just one wind on the rider. This wind we can call the "effective wind" and the angle it hits the rider is known as it's yaw angle.

Given that most of us ride significantly faster than the meteorological wind is blowing, most of the time, the resistance wind tends to dominate. For example, if we ride at 40kph with a 10kph full-on sidewind (meteorological wind approaching at 90 degrees to our ride direction) the effective wind has a yaw angle of just 14 degrees. In fact modelling suggests that somewhere between 50 and 70 percent (let's say 2/3rds) of effective wind yaw angles experienced by a rider are lower than 10 degrees, the faster your ride, the higher this percentage. The same research suggests that a further 30 percent (let's say 1/3rd) of effective wind yaw angles are between 10 and 20 degrees.

You might arrive at the same conclusion after a few trials with this Yaw calculator:

Bike Velocity (KPH)
Wind Velocity (KPH)
Wind Angle (Degrees)
Yaw Angle (Effective Wind in Degrees)
Effective Wind (KPH)
Axial (Head) Wind Component (KPH)
Lateral (Cross or Side) Wind Component (KPH)

The Relevance of Yaw

So why does yaw matter? Life is never simple and it so happens that cyclists, bike frames and wheels, as well as the whole lot together, present different drag profiles depending on the yaw angle of the wind. On the other hand much aero equipment offers less advantage at the lowest (eg zero) yaw angles, hence why aero frame and wheel manufacturers are now particularly keen to demonstrate the advantages of using their equipment in terms of drag reductions at specific, meaningful yaw angles, especially the 0-20 degree kinds that most of us experience, most of the time.

Consider the following extracts from the current Zipp technical literature (left) and from an aero frames review comissioned by VeloNews (right) which graph drag numbers attributed to various aero components at various yaw angles. Note - "AOA" in the first example denotes "Angle of Attack" which is simply aerodynamicists (or aviators) speak for effective wind yaw angle.

What could we conclude from the above?
  • Most cycling equipment, including in these examples, tends to be drag tested with airflow at 30mph so the quoted drag numbers apply only at this speed, they can however be normalised to other speeds. The benefits accruing to an individual rider depend on ability - the faster we ride, the more we benefit from aero equipment.
  • All of the wheels tested by Zipp experienced basically the same drag at 0 degrees yaw (the very left of the chart). To explain this consider whether one 700c wheel looks any different from the next when viewed head-on.
  • Differences between the wheels become more pronounced as the yaw angle increases, peaking in the 10-15 degree range before levels of drag converge again. This is unsuprising - manufacturers know the distribution of yaw angles experienced by most cyclists and design their wheels to be optimal.
  • The aero frames (as complete bikes) tested by VeloNews also display the lowest drag differentials around zero degrees yaw, only in this case "0 degrees" is plotted in the middle of the chart with negative yaw angles off to the left. There may be some merit in testing frames with left and right yaw due to asymmetric design that is less relevant to wheels.
  • Differences between drag applicable to the bikes peaks between 10-20 degrees yaw.
  • For the reaons mentioned above we should be particularly interested in drag differentials in the 0-10 degree range, followed by the 10-20 degree range.
  • Drag savings quoted in terms of grams (or sometimes pounds) can appear quite abstract and have little meaning to the layman. When deciding which wheels to invest in we want to know savings in terms of watts or benefits in terms of speed...

From drag to wattage savings...and speed effects

So what does it mean to save X grams of drag at 30mph, besides what the manufacturer promises us it means? You may have seen a rule of thumb that "50 grams of drag at 30mph is worth 5 watts" but, on a practical level, it is far nicer to be able to transform drag at a specific measurement speed to wattage savings at this or another speed. Some simple rearrangements of the equations of motion that make up cycling power models allow us to do this.

Use the following calculator to find wattage savings applicable to drag numbers, it also calculates "equivalent" CdA (meaning the change in a riders CdA that would be explained by the drag number) since this is one of the intermediate values in the calculation.

Drag
Measured at Speed
Equivalent CdA *  
Target Speed
Watts *

*These measurements assume a "standard" sea level air density of 1.225 kg/m^3

The "advantage" of watts is something you can think about in terms of
  • Training. How hard is it to increase threshold power by X watts?
  • Speed. The speed benefit of "X watts saving" really depends how fast you are assumed to be riding before applying the saving. We suggest the Scenario Model to study the effect of watts on speed, although keep in mind that your wattage number has been derived from a drag number applied to a specific speed.

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