## 8. feb. 2014

### Rolling Resistance Of Bike tires

Earlier we wrote about how the air resistance increases heavily when increasing your speed. Now we will look on the rolling resistance developed between the tires and the road surface. I will try to make you understand how this works. First, we will have to look on how the rolling resistance is found. That can be done by using equation 1 below:

The equation that shows how great the rolling resistance is. The variables are:
• P is the power needed from the rider to keep the velocity. This power is measured in Watt [W].
• Crr is the rolling resistance. This value varies greatly from tire to tire and from the surface being used. There are some few numbers below here from Wikipedia:

 Specific tire Minimum value Maximum value Production bike tires at 8,3 bar on rollers 0,0022 0,005 Typical BMX tires 0,0055 0,0055

• N is the normal force of the bike and its rider against gravity. This force is measured in Newton [N], and can be found by the following equation, equation 2:

In this equation, we have the following variables:
1. m is the mass of you and your bike. This is measured in kilograms [kg].
2. g is the gravitational force. This force is 9,8 m/s2.
3. Cos(θ) is Cosine to the horizontal angle. If you are riding on a flat road that would be 0 degrees which equals 1. So on a flat road this is nothing to worry about. But of your are climbing on a mountain or hill, or descending, it has to be taken into consideration.

But as we already saw with the drag, the power needed is different than the force you are experiencing. The equation for the power required is shown below in equation 3:

There is only one variable that we have not met before. That one is:

1. V is the velocity you are doing. This is easily measured by your bikecomputer http://www.cyclingtipsonline.com/test/bikecomputer-reviews/ . This is measured in meters per second [m/s]. If you want to convert your speed from kilometers per hour to meters per second just divide by 3,6. If you want to change it from meters per second to kilometers per hour, multiply by 3,6.

What this simple equation got, is the rolling resistance multiplied with the velocity. That means that we can put it in equation 1, along with equation 3, and therefore can make it into a single equation, if you want to find the power required at variable speeds. That gives us equation 4:

## Calculation of examples

Lets make a few examples at different speeds. We will take 20 km/h, 30 km/h, 40 km/h and 50 km/h. We say that the rider weighs 70 kg, which is a decent average. The road is also 100% flat. The rolling resistance coefficient of the tires will be 0,003.

If we start off at the 20 km/h, that equals 5,556 m/s. So the equation will be:

As we can see, the rolling resistance will account 11,43 Watt.
At 30 km/h, the equation will be:

Now it has become 17,15 Watt. In a 50 % speed increase, it has increased around 50 % too. At 40 km/h it will be

The value has now increased to 22,87 Watt. As you can see, that is about the double of the value than it was at 20 km/h. So the power required increases linearly with the speed. If you double your speed, you double the power required to overcome the rolling resistance.
However, what if we are having some nice tailwind? How much power will we need to overcome at 50 km/h? That can be found in the equation below:

At 50 km/h the tires are now creating a resistance so great, that you now need to power 28,58 Watt in order to maintain your speed.

Nevertheless, remember, these numbers does not account for much more than just theory. Every tire acts different, and even the smallest difference in production of the same brand of tire can give them two different friction coefficients. And the drag you will experience because of the wind accounts for a much larger value than the tires rolling resistance. Nevertheless, if you want speed, try checking the Continental GP4000S out. They were the fastest clincher tires in the German magazine “Tour” test.
If you want to decrease the rolling resistance as much as possible, ride with a high pressure in your tubes. The higher the pressure the lower the rolling resistance. That is due to the harder the tire will bounce over just the smallest roughness in the surface. But that is different on a mountainbike. On a mountainbike in the forest, a low pressure would actually make you go faster.
But try to read here why you should focuse on buying good tires before spending much more on a pair of wheelset. You will actually be able to win more speed by changing your tires than your wheels!

Written by René