### November 20, 2011

# FLO Cycling - How Velocity Affects Drag

We've been getting a lot of questions about drag lately. Questions like, what is drag, why does it matter, and how does the speed at which I travel effect drag? To answer these questions I have put together a video and a few written examples. I'd recommend you watch the video first. Here we go...

**What is Drag?**

To understand drag, I think it is important to first understand momentum. Momentum is an energy. Momentum exists when you have an object with a mass travelling at a velocity. Something heavy like a train has a lot of momentum because it has a very large mass. Imagine how hard you would have to push a train to get it to stop! Something that is very light, like a cotton ball, has very little momentum. Stopping a flying cotton ball takes very little energy.

When an object (let's say a tennis ball) with momentum hits another object (let's say the fine piece of china your mother warned you to be careful about), the velocity of the tennis ball is almost instantly reduced. The reduction of velocity transfers energy into the piece of china and causes it to move. This results in your mother telling you... well you know the rest of that story.

Air is no different. It's hard to imagine because you cannot see air, but air has a mass and it travels at a velocity. When it hits you on your bicycle, it creates a force and pushes against you. That force is Drag. Here is the equation for Momentum...

Momentum = Mass X Velocity

**Why is Drag Important to You?**

When you are trying to go forward on your bicycle, drag is pushing you back. Drag makes riding your bicycle harder and as a result it slows you down. The more you can reduce your drag, the faster you will go and the easier ride will be. At FLO Cycling, we produce wheels that reduce the amount of drag you experience. This gets you to the finish line faster and makes riding your bike a little easier.

**What is the Equation for Drag?**

The equation for drag is as follows...

Fd = 1/2 x D x V^2 x Cd x A

where...

D = The density of air.

V = The relative velocity of air hitting the object.

Cd = The drag coefficient.

A = The area exposed to the wind.

Density is more or less the mass of the wind hitting you. Velocity is the speed at which the wind is hitting your bike. Cd or the drag coefficient is a value that describes the shape of an object. For example, the Cd of a round object, like a ball is different than the Cd of a square object like a box. The lower your Cd value, the less drag your object creates. Finally, area is the surface area of the object exposed to the wind.

**Why is the Shape of an Object Important?**

If we look at the equation for Drag, we can see that as the Area (A) of an object gets larger, the force of drag increases. Think of carrying a piece of plywood into the wind. If you expose the large flat side of the plywood to the wind, it pushes against you with a large amount of force. If instead you face the skinny end of the plywood into the wind, the force is greatly reduced. When designing cycling wheels, it is important to optimize the surface area of your wheels to help reduce drag.

When riding your bike, the density of air, the drag coefficient and the area remain about the same. For sake of argument, let's assume that they are a constant. This means the drag equation...

becomes...

Velocity is the most significant variable effecting the drag you experience. The fact that it is squared, makes it even more significant. Let's take a look at how you calculate your velocity and how it effects drag.

When calculating drag, velocity is not simply the speed at which you are travelling on your bike. 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 is know as relative velocity. Let's take a look at two pictures to help us understand relative velocity.

In this example the cyclist is travelling at 15mph and the wind is travelling in the opposite direction at 5mph. The relative velocity is therefore equal to...

In this example the cyclist is travelling at 15mph but the wind is travelling in the same direction at 5mph. The relative velocity is therefore equal to...

When testing our wheels in the A2 Wind Tunnel, our relative velocity was 30mph. This is equivalent to you riding your bike at 15mph with a 15mph head wind. Let's look at the amount of drag produced by a FLO 60 vs. a Standard Training Wheel at 15 degrees of yaw.

Drag produced by a

Drag produced by a

The FLO 60 in this situation saves you

Remember that velocity in the drag equation is squared. This means if velocity doubles, your drag will be increased by 4 times! Let's see what happens if we increase our rider speed to 22mph and leave our head wind at 15mph.

Let's first calculate our relative velocity...

Next, let's determine the constant in our drag equation for each wheel using our 30mph numbers. Remember the equation from above...

**How does Velocity Effect Drag?**When riding your bike, the density of air, the drag coefficient and the area remain about the same. For sake of argument, let's assume that they are a constant. This means the drag equation...

Fd = 1/2 x D x V^2 x Cd x A

becomes...

Fd = Constant x V^2

Velocity is the most significant variable effecting the drag you experience. The fact that it is squared, makes it even more significant. Let's take a look at how you calculate your velocity and how it effects drag.

**Relative Velocity**When calculating drag, velocity is not simply the speed at which you are travelling on your bike. 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 is know as relative velocity. Let's take a look at two pictures to help us understand relative velocity.

In this example the cyclist is travelling at 15mph and the wind is travelling in the opposite direction at 5mph. The relative velocity is therefore equal to...

Rider Speed - Head Wind

(15mph) - (-5mph) =

**20mph**In this example the cyclist is travelling at 15mph but the wind is travelling in the same direction at 5mph. The relative velocity is therefore equal to...

Rider Speed - Head Wind

(15mph) - (5mph) =

**10mph****Let's Calculate some Drag.**When testing our wheels in the A2 Wind Tunnel, our relative velocity was 30mph. This is equivalent to you riding your bike at 15mph with a 15mph head wind. Let's look at the amount of drag produced by a FLO 60 vs. a Standard Training Wheel at 15 degrees of yaw.

Drag produced by a

**Standard Training Wheel = 250 grams**Drag produced by a

**FLO 60 = 40 grams**The FLO 60 in this situation saves you

**210 grams**of drag!**Velocity is Squared... That's a Big Deal**Remember that velocity in the drag equation is squared. This means if velocity doubles, your drag will be increased by 4 times! Let's see what happens if we increase our rider speed to 22mph and leave our head wind at 15mph.

Let's first calculate our relative velocity...

**Relative velocity**= 22mph + 15mph =

**37mph**

Next, let's determine the constant in our drag equation for each wheel using our 30mph numbers. Remember the equation from above...

Fd = Constant x V^2

**Standard Training Wheel...**
Fd = Constant x V^2

250(grams) = Constant x 30(mph)^2

250 = Constant x 900

Constant = 250/900

**Constant = 0.278**

**FLO 60...**
Fd = Constant x V^2

40(grams) = Constant x 30(mph)^2

40 = Constant x 900

Constant = 40/900

**Constant = 0.044**

Let's now calculate the force of drag at a relative velocity of 37mph.

**Standard Training Wheel...**
Fd = Constant x V^2

Fd = 0.278 x 37^2

Fd = 0.278 x 1369

**Fd = 381 grams**

**FLO 60...**

Fd = Constant x V^2

Fd = 0.044 x 37^2

Fd = 0.044 x 1369

**Fd = 60 grams**

Now the FLO 60 is saving you

**321 grams of drag!**This is 111 grams more that it was saving you at a relative velocity of 30mph.__This means aerodynamic wheels become increasingly more important as the relative velocity increases.__**Graphing the Data**

Here is a table to show the Drag of a FLO 60 and a Standard Training Wheel vs. the relative velocity. Notice how much faster the grams of drag increase for a standard wheel! As your speed or the wind speed increases, aero wheels become much more important! At a relative wind speed of 60mph, a FLO 60 will save you over 800 grams of drag.

**Conclusion**

Drag to a cyclist is a very big deal. Simply put, reducing drag will get you to the finish line much faster. Using aerodynamic wheels like our FLO 60, 90, DISC and CLIMBER will greatly reduce the drag that you experience.

To learn more about cycling wheel aerodynamics, check out our post here http://bitly.com/mlu0Bm

To learn more about cycling wheel aerodynamics, check out our post here http://bitly.com/mlu0Bm

If you have any additional questions about drag please feel free to post them in the comments below. 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.

Take care,

Chris

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## 6 comments :

Did you run any other wheels when you did your wind tunnel testing? Your Flo 60 drag numbers look a little lower than the ones published by Zipp for the Firecrest 404's.

Chris G.,

Thanks for leaving tour comment. We tested our FLO 60, 90, DISC, CLIMBER, and a Mavic open pro. As a start up business we didn't have the budget to test any additional wheels.

All the best,

Chris

How is a 5mph headwind 15degrees of yaw angle? It looks like you are making up yaw angle numbers to show off where your wheels perform the best.

Also, it looks like according to this the 15degrees number is way off.

http://biketechreview.com/forum/1-general-discussion/26549-yaw-angle-versus-height-above-ground

d20rider,

I apologize, but I can't fully understand what you are asking me. I'm not sure you understand what we mean when we are talking about "wind speed" and "yaw". Let me try to address your questions as in an attempt to clear some things up...

How is a 5mph headwind 15degrees of yaw angle?Headwind and yaw are different things. "Wind speed" or "headwind" is the speed of the wind hitting you on your bike. "Yaw angle" is the relative angle at which the wind is hitting you. To clarify, I did not say that 5mph of headwind is 15 degrees of yaw. My graph is showing a variety of relative windspeeds at 15 degrees of Yaw.

It looks like you are making up yaw angle numbers to show off where your wheels perform the best.I'm not sure where you are getting this idea either? I haven't "made anything up" in an attempt to make our wheel appear better. I'm simply showing how a varied windspeed relates to drag at 15 degrees of yaw.

Also, it looks like according to this the 15degrees number is way off.I read through your article you referenced. I don't see how it relates to what I am discussing. Again... 15 degrees of yaw is the relative angle at which the wind is hitting you. The article you are referencing appears to be defining "yaw" differently.

I think your confusion is simply based on the definition of the terms being used. Based on your comment, I am under the impression that you feel I am trying to mislead you. I wanted to clarify since that is not what I am trying to do. For a better understanding of what I am discussing, you may want to check out our "Cycling Wheel Aerodynamics Tutorial" here..

http://flocycling.blogspot.com/2011/05/flo-cycling-wind-tunnel-results-and.html

Don't hesitate to ask any additional questions should you have them.

Chris

Let's Calculate some Drag.

When testing our wheels in the A2 Wind Tunnel, our relative velocity was 30mph. This is equivalent to you riding your bike at 15mph with a 15mph head wind. Let's look at the amount of drag produced by a FLO 60 vs. a Standard Training Wheel at 15 degrees of yaw.

From the article.

If you are riding at 15mph and you have a 15mph headwind, the yaw angle is 0.

Even if the wind is blowing directly from the side at 15 mph and you are riding at 15mph the yaw angle is going to be lower than just comparing wind speed to bike speed. From the biketechreview page the lower you are to the ground the lower the wind speed will be.

The first post in that thread shows the Hellman formula and how it affects the wind speed at various heights on a bicycle. If there is a 15mph wind outside (measured by weather stations at a height of 10meters above the ground), the wind at your wheels is going to be much less.

The crosswind shows an ideal situation for producing the highest possible yaw angles. How many times do we ride in a pure crosswind? How often does the road stay perfectly straight in those circumstances? And there will likely be trees, houses, hills all helping to buffer the wind. I think your 15degree estimation of yaw angle is vastly high (especially as you said if the rider is riding into a headwind). True, these wheels do well at 15degrees of yaw angle. . but we shouldn't be told that is where the majority of our riding happens.

At race speeds (closer to 25mph, the yaw angle becomes even less)

d20rider,

If you are riding at 15mph and you have a 15mph headwind, the yaw angle is 0.

In that definition of the term you are correct. Perhaps my explanation wasn't detailed enough. I should have said, relative speed of 30 mph at 15 degrees of yaw. Sorry for not being clear enough.Even if the wind is blowing directly from the side at 15 mph and you are riding at 15mph the yaw angle is going to be lower than just comparing wind speed to bike speed. From the biketechreview page the lower you are to the ground the lower the wind speed will be. The first post in that thread shows the Hellman formula and how it affects the wind speed at various heights on a bicycle. If there is a 15mph wind outside (measured by weather stations at a height of 10meters above the ground), the wind at your wheels is going to be much less.

In my example, the wind speed at the wheels is 15mph. I didn't say anywhere that I took the measurement from a 10 meter weather station, so I'm not sure where you are getting that idea.The crosswind shows an ideal situation for producing the highest possible yaw angles. How many times do we ride in a pure crosswind? How often does the road stay perfectly straight in those circumstances? And there will likely be trees, houses, hills all helping to buffer the wind. I think your 15degree estimation of yaw angle is vastly high (especially as you said if the rider is riding into a headwind). True, these wheels do well at 15degrees of yaw angle. . but we shouldn't be told that is where the majority of our riding happens.

I used 15 degrees of yaw simply for an example. I had to pick a number. I could have picked 10 or 20 or 4.6, but I had to stick with something when writing the article. You may feel that our 15 degree estimation is high but many others would disagree with you.

I'll also mention that our estimated drag/time savings on our Aerodynamics pages are based off of an average. We call it "Net Drag Reduction Value" (NDRV). We did this because we know cyclists don't always ride at specific yaw angles. As you said, there are trees and hills and turns and gusts of wind etc. NDRV takes an average of all yaw angles when calculating savings.

At race speeds (closer to 25mph, the yaw angle becomes even less)

That is correct. Higher speeds equal lower yaw angles.If you would rather I calculate savings at a different yaw angle for you, I would gladly do so. Just let me know.

Chris

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