### May 8, 2011

## FLO Cycling - Wind Tunnel Results and Cycling Wheel Aerodynamics Tutorial

**Introduction**

When we set out on our journey to design aerodynamic cycling wheels, we asked ourselves, “what makes a wheel aerodynamic?” We soon learned there wasn’t a real answer. After hours of research, computational fluid dynamics testing, and a trip to the A2 wind tunnel, we now know what makes a cycling wheel aerodynamic. Below are several paragraphs discussing how we designed our FLO Cycling wheels and of course our

Be sure to check out our latest wind tunnel results on the all new FLO wheels. You may also find Part 1 and Part 2 our tire study of interest. In our tire study, we studied the combined resistance of aerodynamics and rolling resistance on nearly 20 tires.

**w****ind tunnel results**. For those who are interested in understanding the science that goes into designing aero wheels, we have added an additional section to the end of this blog post titled "**Aero Wheel Tutorial.**" As always, questions and comments are more than welcome!Be sure to check out our latest wind tunnel results on the all new FLO wheels. You may also find Part 1 and Part 2 our tire study of interest. In our tire study, we studied the combined resistance of aerodynamics and rolling resistance on nearly 20 tires.

**FLO Cycling Design**

The picture below shows the progression of aerodynamic wheel shapes. The V-Notch design was one of the earliest aerodynamic wheel shapes on the market. This wheel displayed a reduction in aerodynamic drag but is known for being unstable in crosswinds. Many manufacturers still use this technology today.

Designers next released what was known as a toroidal shape. The toroidal fairing flared out and got wider than the brake track before coming to a point. This design showed an even greater reduction in aerodynamic drag and improved crosswind stability

**FLO Cycling Symmetrical Design**

In our opinion, the largest downside to both the V-Notch and early toroidal design is that they come to a point. The leading edge on the front half of any wheel is the tire. A tire is a bulbous circular object. If we want to create even side force on the front half and the back half of the wheel, we assumed that the leading edge on the back half of the wheel would have to also be a bulbous circular object. By removing the “point,” we have been able to create a balanced aerodynamic system. On a FLO Cycling wheel, the leading edge on the front half of the wheel (the tire) is nearly identical to the leading edge on the back half of the wheel (our wide toroidal shape). This design reduces the aerodynamic drag even more than the early toroidal shapes and greatly improves crosswind stability. FLO Cycling wheels are nearly symmetrical from front to back. The result of this symmetry is superb aerodynamics and superior crosswind stability.

**Net Low Drag Technology**

When we sat down to design our wheels we observed the aero data published by other companies and noticed a trend. Their wheels became very aerodynamic at a specific yaw angle. Unfortunately, a few degrees in either direction of that yaw angle caused the drag to rise quickly. This produces good results in a controlled environment like a wind tunnel, but doesn't necessarily help in the real world. We'd all love to ride our next race at the optimal wind angle, but mother nature simply won't let that happen.

Our goal was to produce wheels that became aerodynamic and stayed aerodynamic for as long as possible. We knew that roughly 80% of a cyclist's time is spent riding in yaw angles between 10 and 20 degrees. During our CFD analysis we tweaked our wheel shapes to be as aerodynamic as possible throughout that 10 degree sweet spot, and not at a specific point. The wind tunnel results were remarkable. As an example, our FLO DISC wheel experiences negative drag from 12 to 24 degrees of yaw.

A lot of companies claim to have the fastest wheels in the world. At specific angles, using specific tires, and in a wind tunnel, they certainly do. They also say that at that specific angle the wheel will save you X amount of seconds at your next race. Unfortunately, the wind will not be blowing only at 12.6 degrees of yaw at your next race.

At FLO Cycling we wanted to define a useful term. Since we know we spend roughly 80% of our time racing between 10 and 20 degrees of yaw, we feel it is best to calculate a weighted average of drag reduction. A cyclist would then have an excellent idea of how many seconds a FLO Wheel will save them regardless of the wind angle. We call this value the

**Net Drag Reduction Value (NDRV)**.
Below are the

**NDRV**of our FLO wheels and the optimal reduction value assuming mother nature is only blowing at the perfect angle all day. These values are the amount of grams saved when compared to a standard box section rim (Mavic Open Pro - 32 Spokes).**FLO CLIMBER**

**NDRV:**78.3 grams - 31.3 seconds over a 40km time trial OR 2 minutes and 21 seconds over an Ironman.

**Optimal Reduction:**88.3 grams - 35.3 seconds over a 40km time trial OR 2 minutes and 39 seconds over an Ironman.

**FLO 60**

**NDRV:**175.3 grams - 70.1 seconds over a 40km time trial OR 5 minutes and 16 seconds over an Ironman.

**Optimal Reduction:**210.1 grams - 84.0 seconds over a 40km time trial OR 6 minutes and 18 seconds over an Ironman.

**FLO 90**

**NDRV:**172.1 grams - 68.8 seconds over a 40km time trial OR 5 minutes and 10 seconds over an Ironman.

**Optimal Reduction:**202.1 grams - 80.9 seconds over a 40km time trial OR 6 minutes and 04 seconds over an Ironman.

**FLO DISC**

**NDRV:**253.7 grams - 101.5 seconds over a 40km time trial OR 7 minutes and 37 seconds over an Ironman.

**Optimal Reduction:**319.9 grams - 128.0 seconds over a 40km time trial OR 9 minutes and 36 seconds over an Ironman

Without further ado, here are the FLO Cycling Wind Tunnel Results...

**Aero Wheel Tutorial**

Let’s start by defining some terms:

**Yaw Angle**

A yaw angle is the angle at which the wind interacts with the wheel. Take a look at the pictures below. In

**Figure A**, the wind (blue arrow) is hitting the wheel at 0 degrees. This is known as 0 degrees of yaw, and what you experience when the wind is blowing straight at you. In**Figure B**, the wind is now interacting with the wheel at a 20 degree angle. This is known as 20 degrees of yaw and the cyclist would a feel a combination of headwind and side wind.
Let’s start with a visual. Imagine a canoe moving through a calm lake. The front of the canoe is the first part of the boat to cut through the water. It is therefore defined as the “leading edge." A wheel in the wind is no different. Remember, air is a fluid just like water.

A wheel can have two leading edges. The tire at the front of the wheel, and the carbon fiber fairing at the back of the wheel. When a wheel is at 0 degrees of yaw, the front of the wheel is the only leading edge. This is because the back of the wheel is “hiding” behind the front of the wheel (see

**Figure C**). When a yaw angle of greater than 0 degrees is introduced, we now have two leading edges.**Figure D**shows the wind at 20 degrees of yaw. The back of the wheel can no longer “hide” behind the front of the wheel and sees its own air. It is therefore defined as a leading edge.Figure C |

Figure D |

Drag |

Drag is defined as the force on an object that resists its motion through a fluid. Let’s use another water example. If you stand in waist deep water and try to run forward, the force you feel holding you back is drag. Air also has drag, just not as much as water.

**Lift**

Lift or “side force” is one of the most important forces to consider when designing aerodynamic cycling wheels. To help you better understand the three main components of lift, let’s shift our focus to the skies and talk about airplanes.

Figure E |

The wings of an airplane allow it to fly, but how? To answer this, let’s look at the forces acting on an airplane (

**Figure E**). Thrust is the force generated by the engine of the airplane to move it forward. Drag is the force exerted by the air that resists the forward motion of the airplane. Let’s ignore these two forces for now.
Gravity is the earth’s attractive force that wants to keep the airplane on the ground. Lift is the force we need to create in order to get the plane off the ground. To take flight, we need the lift force to be greater than the gravitational force. Lift is generated by the wing. A wing has three major components that contribute to the lift force it produces. Those three components are:

1. The shape of the wing.

2. The wing’s angle of attack.

3. The velocity or speed of the wing.

The shape controls the way the air (fluid) moves around the wing. By controlling the airflow, we can create areas of high pressure below the wing, and areas of low pressure above the wing. Anytime there is a difference in pressure on opposite sides of an object, the high pressure side pushes the object towards the low pressure side. Think of a balloon. The more air (pressure) you blow inside of the balloon, the bigger the balloon gets. This is because the high pressure is pushing the inside of the balloon out. In order to take flight we have to create a high enough pressure under the wing to lift the plane off of the ground.

The angle of attack is the angle that the wing moves through the air. This is the same as the yaw angle of a wheel. As you increase the angle of attack, you increase the lift force until you reach the critical angle of attack. The critical angle of attack is the angle that produces the maximum lift. Think of sticking your hand out of the window of a moving car. By turning your hand up or down (changing the angle of attack), you can make your hand rise or fall. If you turn your hand too far in either direction, it no longer moves up or down but instead straight back.

Finally, we have the velocity or speed at which the wing travels through the air. The simple answer here is the faster you go, the more lift you create.

**Wheel Design**

When designing effective aerodynamic race wheels there are, in our opinion, two very important points to consider. The first point is the reduction of drag. In order to be fast, the wheel must reduce aerodynamic drag as much as possible. The second point is the ride quality and stability of the wheel. Anyone who has ridden deep wheels in a strong side wind knows they can be a challenge to control. Therefore, it is important to design a wheel that has good crosswind stability.

**Side Force (Lift) and Drag**

In the world of cycling, lift is called side force.

**Figure F**shows a wheel at 0 degrees of yaw. In this case the wheel only experiences drag. Since the wind flows evenly around both sides of the wheel, side force is equal to 0.**Figure G**shows a wheel at 20 degrees of yaw. Thinking back to our airplane example, we have increased the angle of attack. This produces a higher side force on the side of the wheel facing the wind and produces lift.

Let’s now consider the side forces that a standard training wheel experiences. Because a standard training wheel has very little rim depth, it generates very small side force. For the sake of argument, the drag is more or less equal to the side force.

An aero wheel, however, has a much deeper rim profile and an increased surface area. The increased surface area generates a higher drag force. An efficient fairing shape will increase the side force. The key is to design a fairing shape that produces a higher percentage of side force relative to drag.

Why do we want side force? Let’s start with vector forces. When a force pushes on a surface at an angle, a portion of that force pushes the object in the X direction and a portion of that force pushes the object in the Y direction. Take a look at

**Figure H**.
Let’s look at the vector components of side force and drag acting on a wheel.

**Figure I**shows that the Y component of side force actually opposes the Y component of drag. In theory, if we can generate a side force high enough relative to drag, the Y component of side force will be greater than the Y component of drag. When this happens, the wheel will actually be pushing you forward. This is known as negative drag.Figure I |

Here are two numeric examples:

__Standard Box Rim Wheel__
Total Drag Force = 100g

Drag Force Y Component = 93.97g

Total Side Force = 100g

Side Force Y-Component = 34.20g

**Resultant Drag Force**= (Drag Force Y-Component) - (Side Force Y-Component)

**Resultant Drag Force**= 93.97g - 34.20g

**Resultant Drag Force**= 59.77g

__Aerodynamic Wheel__
Total Drag Force = 150g

Drag Force Y Component = 140.95g

Total Side Force = 450g

Side Force Y-Component = 153.90g

**Resultant Drag Force**= (Drag Force Y-Component) - (Side Force Y-Component)

**Resultant Drag Force**= 140.95g - 153.95g

**Resultant Drag Force**= -12.95g

**Cross Wind Stability or Yaw Torque**

Imagine a seesaw on the playground. Let’s put a child weighing 50 lbs on one side and a child weighing 70 lbs on the other side. We all know that the 50-lb child will quickly rise up in the air.

In theory the front wheel of a bicycle is the same. We have the front half of the wheel, the back half of the wheel, and the steering axis. If we push on the front half of the wheel and leave the back half alone, the wheel will turn around the steering axis in the direction of your push. Take a look at

**Figure J**.
If we are going to make a wheel that is stable in cross winds, we want the side force on the front half of the wheel to be equal to the side force on the back half of the wheel. This would be the same as placing a 50-lb child on both sides of the seesaw. This will prevent any turning of the wheel. If the side force on the front of the wheel is greater than the side force on the back of the wheel, any gust of wind will cause the wheel to quickly turn in one direction.

We hope this tutorial has helped you understand the basics of cycling wheel aerodynamics. For more great content, please register for our free monthly newsletter at the top of the column on the right. We send links to all the articles we post during the month. If you have any questions, please feel free to ask!

All the best,

Jon and Chris Thornham

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