### November 12, 2012

# FLO Cycling - Cycling Wheel Aerodynamics - How Speed, Time, and Power are Affected by Reducing Drag

*Note: For an updated version of this blog article displaying the time savings for our new 2016 model wheels, read this article.*

There's a list of common questions we see from people trying to understand the importance of cycling wheel aerodynamics. These questions include the following:

1. Your CFD simulations and wind tunnel tests used wind speeds of 30mph. If I don't ride at 30mph, do aerodynamic race wheels make sense for me?

2. How much faster will I go with race wheels compared to my stock wheels?

3. How much of a power saving will I see if I buy aerodynamic cycling wheels?

These are all great questions and are most commonly answered with rules of thumb. These include the following:

1. If you are travelling 30mph, you will save 40 seconds over a 40k if you reduce the drag by 100 grams.

2. 50 grams of drag reduction equates to 6.5 watts of power savings.

These numbers are true, but it does not help someone understand why or how these numbers relate to their specific case. This article will walk through all of the equations and show how and why these numbers are true. I have also made tables that show how drag reduction affects you at your speeds. It's counter intuitive, but the slower you are, the more time you will save by upgrading wheels and reducing your drag. There is quite a bit of math in this post but don't fret. I'll do my best to walk through each step.

**Relative Velocity**

Before we get into the math, there is an important concept you should understand. This is relative velocity. When calculating drag, your speed is not simply the speed at which you are travelling on your bike. Relative velocity is the combination of the speed at which you are travelling on your bike and the velocity of the wind. This combination of velocities are known as the relative velocity. If you are traveling 15mph into a 5mph head wind, your relative velocity would be 20mph. If you were travelling 15mph with a 5mph tail wind, your relative velocity would be 10mph. For a more detailed explanation on relative velocity, you will find this post helpful.

**How Drag is Calculated and its Components**

Drag is defined as the force on an object that resists its motion through a fluid. 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.

Drag is calculated with the following formula:

Drag Equation |

The variables of the equations are defined as follows:

Variables of the Drag Equation |

Most of the variables are self explanatory but there are two I will describe in more detail.

**Drag Coefficient**

Drag coefficients are associated with shapes. The lower the drag coefficient, the more aerodynamic the item is. The drag coefficient is determined in wind tunnel tests. Here is a list of common shapes and their associated drag coefficients.

Drag Coefficients for Common Shapes |

Drag coefficients are not limited to simple shapes. You can calculate a drag coefficient for any object. The following shows the drag values associated with human powered vehicles. For the rest of this post we will be using the "Racing (Fully Crouched)" data. This has a CD of 0.88 and frontal area of 3.9ft^2.

Drag Coefficients for Human-Powered Vehicles |

**Frontal Area**

Frontal area is commonly described as the area that sees the wind. As an example, imagine standing in a strong wind. If you were facing the wind, it would come in contact with the front half of you body. The back half of your body and your sides would not be in direct contact with the wind. In this situation, the front half of your body would be the frontal area. If you were to turn 90 degrees to the right, your left side would now feel the wind and would become the area in direct contact with the wind. This would be the new frontal area.

All objects have a frontal area, and for this post we will be using the value in the table above of 3.9ft^2 or 0.362m^2.

**If you are Traveling at 30mph, you Will Save 40 Seconds Over a 40k by Reducing the Drag by 100g**

To prove this is true let's calculate the drag experienced by a cyclist using the CD and frontal area in the table above. Let's first show the numbers used for the equation. (Note the tags like D Original are used to identify different values. As we move on we will use multiple CD values and this is a way to identify them.)

Using these values we can calculate the drag experienced by a cyclist in the "Racing (Fully Crouched)" position.

This says that a cyclist will experience an average of 3,580.423 grams of drag when riding at a relative velocity of 30mph.

Now let's reduce the drag value by 100g and see what we get.

Now that we have calculated the new drag value, we can rearrange the drag equation to calculate the new CD value. It should be pointed out that in order to reduce the drag we have to lower the CD value.

Using the new equation we can calculate the new CD value when the drag is reduce by 100g.

With the new CD value we can now calculate the new speed seen by the cyclist by again rearranging the drag equation. In this example we are using the original drag force and the new CD value to calculate the new velocity. (Note: It should be pointed out that when velocity increases the drag also increases. This means the calculation is not perfect but it does provide a very close estimate. To know the exact number you would need to study the configuration in a wind tunnel).

Now we can calculate the new velocity. Let's see what we get.

Now that we have the new velocity we can determine the time savings over a 40km race.

From this we can see that the industry standard stating that you will save 40 seconds over a 40km when traveling 30mph is true. There is a difference of 1.95 seconds but this difference could easily be explained by using a different frontal area, different CD values or taking the affect the increased velocity had on the drag value into consideration.

**How Much Faster Will I Go at the Speed I am Traveling?**

As stated above, it's counter intuitive but you actually save more time the slower you travel. The cool thing about the calculations above is that you can easily calculate the new speeds and time savings for any original speed you like. A CD value is a CD value no matter what speed you are traveling and remains constant for all of the calculations. I have put together a table that shows the time savings and new speeds for each original speed from 1mph to 30mph when you use the new CD value. The values for a 40km and an Ironman in seconds are listed below.

Time Savings at Any Speed when Removing 100g of Drag at 30mph |

The next best question is how much time will I save with a FLO 30, FLO 60, FLO 90, and FLO DISC. The following shows the savings for each wheel. Remember if you have two wheels multiply the savings by two.

**FLO 30 Time Savings at Any Speed**

**FLO 60 Time Savings at Any Speed**

**FLO 90 Time Savings at Any Speed**

**FLO DISC Time Savings at Any Speed**

**Proving 50 grams of Drag Reduction Provides 6.5 watts of Power Savings at 30mph**

This one is an easy one compared to the last one. Let's look at the equation for power.

Using the equation for power we find the following.

This proves that the standard is true and shows you how to calculate the value.

Here is how much power the FLO Wheels can save you at a relative velocity of 30mph.

Power Savings at 30mph |

**Summary**

I hope that you've found this article helpful and that you didn't get lost along the way. There is a lot to take in, but it should help you to better understand the importance of aerodynamics and how they affect you and your time on the bike.

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. Please ask questions and post your thoughts below.

Take care,

Jon

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## 17 comments :

Drag force is a function of Cd. So why is the drag force in the tables the same for both the FLO and Mavic?

That's a good question. The reason is that we are solving for the increase in velocity and not the drag force. When the equation is rearranged to solve for velocity, we use the original drag force to find the new velocity. If we used the drag force found at 30mph for the new CD, we would get the same 30mph answer. The increase in drag allows us to find the new velocity. Does that make sense?

Sorry to get complicated, but do you take into account the relative velocity of the wheels in respect to the frame? What I mean, is that if the bike is moving forward at 20mph (with no wind), a single point on the wheel will be moving with a relative forward velocity of 40mph at the top of the wheel, and 0mph where the wheel contacts the ground. These equations here are of course a simplification, but I wonder if it's taken into account in your computer models, and whether you use a spinning wheel or a static wheel when you test in the wind tunnel. Cheers, great work by the way, I hope to order some of your wheels soon!

See if I have this right, so a switch from a FLO 60 rear to a FLO Disc at 25 mph for a 10k TT we're talking about 10 seconds savings?

Thanks,

John

Is there a good reason why FLO 90 is worse than FLO 60 (I know nothing except that I suspect the number is the rim height, and higher is typically better)?

Nick,

That's a great question. The CD values we used are for a cyclist. All of the tests we perform on the wheels use a spinning wheel. The CFD model and the wind tunnel both use 30mph. We get a CD value from the wheel by itself in both situations.

Jon

John,

That is correct. Over a 10k you would save approximately 10 seconds by switching to a FLO DISC from a FLO 60.

Jon

Based on the data you have on the FLO60/90 it would seem you can make a pretty good guess as to where the FLO30 will plot on your drag data chart?

gnicholson,

When we test in CFD we do not add the spokes and hubs. Our most recent CFD testing used modified parameters to enhance the mesh and produce a better result. These two factors make it challenging to predict what will happen in the wind tunnel. Our goal is to drop below 100g of drag and stay low for much more of the 10-20 degree yaw angle range. Our results from CFD show that this appears to be the case. You will notice that the wind tunnel data for the FLO CLIMBER and the CFD data show different results. This will be what we clarify with the FLO 30 in the wind tunnel. I hope that makes sense.

Jon

I know this is basically a back-of-napkin "calculation" but, "Remember if you have two wheels multiply the savings by two."

This can't be even close to right, can it?

Nate,

Aerodynamics can only truly be understood with testing. We test our wheels individually when we are in the wind tunnel and compare the results to the drag produced by a standard box wheel. Any time you add another element to a drag test you alter the CDA. Frame interaction, rider postion, tire selection etc all have an effect on the total system drag reduction you will experience.

Theoretically if you were to send two wheels down the road by themselves you would save twice the time. Once you introduce a frame and a rider things change quickly. The only way to know for sure would be to test the entire system. The main goal is to show the amount of time savings you would experience if you were to reduce "x" number of grams of drag.

Also remember that we used a CDA for a cyclist and not just a single wheel. Ultimately the calculations are pretty accurate but remember the system needs to be tested to know for sure.

Take care,

Jon

nice

Thanks Wood Works!

Jon

An update on savings at any speed in relation to the new line of wheels ( carbon clincher) would be awesome! 😊

Thank you in advance!

Emil

Emil,

I will be updating this in the future. I don't have a date yet but it will happen.

Take care,

Jon

Emil,

We have posted the update you requested. I hope you enjoy it.

http://flocycling.blogspot.com/2016/06/flo-cycling-how-much-time-will-flo.html

Take care,

Chris

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