Aerodynamics And Rolling Resistance At Different Rider Speeds

I was recently working on a problem to determine the number of watts required to overcome aerodynamic drag and rolling resistance at different rider speeds. What I found surprised me. While I know aerodynamics grows quickly, I didn’t know how quickly.

Our FLO All Sport and Gravel wheels were designed to optimize both aerodynamic drag and rolling resistance. The resulting products are the fastest we’ve ever made. To show the significance of aerodynamic drag and rolling resistance to you, a cyclist, I wrote this article which walks through the math and the importance each is to your overall speed.

The Chung Method

For starters, let’s refer to the great work by Robert Chung. The Chung Method breaks down the number of watts required to propel a bike forward at a specific ground speed.

This equation can be broken down into four parts.

This gives us the equation of:

This can be further broken down to:

Each variable of the equation above is listed below:

v = speed in m/s (i.e., “ground” speed)
m = total mass (kg) of rider + bike
g = 9.81 m/sec2
Crr = coefficient of rolling resistance
s = slope
a = acceleration
ρ = air density
v = “air” speed of bike air
CdA = drag area

Assumptions For Our Example

To make things a bit easier to understand we are going to assume that the slope is 0 degrees and that our acceleration is 0. This will allow us to simplify the equation to the following:

Using this equation, we can see that if given a ground speed and an air speed, we can determine the total watts required to ride at that speed. We can also see how many watts account for aerodynamics and rolling resistance.

In this example, we are going to assume that the wind speed is 0 which means our Vair is going to equal the ground speed. We will also assume the following about our rider so we can calculate the watt value.

Crr = 0.0026
m = 81 kg
v = 10 mph or 4.4704 m/s
CdA = 0.35
ρ = 1.225

Results From 1-30 Miles Per Hour

Now that we understand how the equation works, the table below shows the watt values required to be overcome for speed from 1 to 30 mph. Notice how rolling resistance starts higher, the two meet around 7mph, and then aerodynamic drag takes off quickly. This is because of the cubic factor of the velocity component of the aerodynamic drag.

Final Thoughts

As you can see, both aerodynamics and rolling resistance are important when you are trying to improve your overall speed. We can see that the faster you go, the more it matters. In a few weeks we will look deeper into rolling resistance and how it is affected by speed when the Crr value changes. This will highlight the importance of a wheel that lowers your rolling resistance like the FLO All Sport and Gravel Wheels. After, we will cover the aerodynamic component in more detail.

Let us know your thoughts on how rolling resistance and aerodynamics affect your total watt output.

12 comments

Michael,

The coefficient of rolling resistance is a dimensionless constant that is used to find the force required to roll an object forward. It is measured in a lab setting where there are a number of known inputs. Crr can then be solved for as the unknown.

Ride safe,

Jon

Jon Thornham November 18, 2020

Aivars,

Aerodynamic drag is calculated by looking at relative velocity. This article talks about it.

https://flocycling.com/blogs/blog/flo-cycling-cycling-wheel-aerodynamics-how-speed-time-and-power-are-affected-by-reducing-drag#:~:text=Relative%20velocity%20is%20the%20combination,relative%20velocity%20would%20be%2020mph.

Ride safe,

Jon

Jon Thornham November 18, 2020

Dr. B,

In the table I am looking at I see they cross at nearly 10mph. At 7mph I see 12.93 and 6.97.

Ride safe,

Jon

Jon Thornham November 18, 2020

Jason,

You are right. We’ve studied these factors in multiple different situations and have written about them here on the blog. We recommend warming your tires up before finalizing your tire pressure.

Ride safe,

Jon

Jon Thornham November 18, 2020

Steve,

To get km/h you can multiply any value you want by 1.6. This will give you the km/h speed.

Ride safe,

Jon

Jon Thornham November 18, 2020

Tom,

Thanks for the input. You are right, Crr changes at speed an on different surfaces. It also changes based on the tires characteristics.

Yes, the 0.0026 is really low but it was for calculation purposes only.

Ride safe,

Jon

Jon Thornham November 18, 2020

What is the Coefficient of rolling resistance?
How is this value found?

Michael Drury November 18, 2020

Does the headwind’s aerodinamic effect equals that of objects own speed’s at 0 headwind?

Aivars November 18, 2020

Actually rolling resistance meets drag at 10 mph not 7 mph based on your chart data.

Dr. B November 18, 2020

What about the effects of ambient temperature, road temperature and air temperature of the tyre when it was inflated. Which in some cases is welll before a race or indoors. Let’s not forget actual tyre temp. So does a 30 deg C tyre roll faster than a 10 deg C as it’s more supple, both with the same pressure?

Jason Swann November 18, 2020

Hi, nice article, can you gives speeds in kph as well? Thanks!

Steve November 18, 2020

I use the Chung method often to calculate both CdA and Crr. With latex tubes and 25 mm GP5000 on pretty good pavement, I can average about 0.0042 for Crr and 0.005 on less than good pavement. I need about 285-290 watts to travel 30 mph on a fast recumbent bike and what I have learned is Crr is not entirely a constant. Depending on tires, one will see a much higher Crr at 30-35 mph compared to 20 mph but I have never come close to 0.0026 that you use in your example, whether on an upright or recumbent bike.

Tom November 18, 2020

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