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].
• C_rr 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

Read more: http://www.cyclingtipsonline.com/news/rolling-resistance-of-bike-tires/

The Aerodynamics Of A Bikerider

There are two main reasons why you are not travelling with 100 km/h when you are riding on your bike. One of these is rolling resistance, but the other by far the biggest factor, is the drag you are experiencing due to the wind resistance. This force increases exponentially with your speed, where the rolling resistance on your tires only increases linearly. Therefore, as the speed increases, the wind resistance becomes a bigger and bigger factor compared to the rolling resistance.

So yes, aerodynamics is a very important factor in the world of cycling. That is why we are seeing pro’s having drop-shaped helmets and special time trial bars, making their wind resistance as low as possible. The tight lycra clothes all riders are using is also helping on lowering the wind resistance. Loose clothes will be like having a parachute slowing you down.
One of the newest trends are road frames, that are becoming more and more aerodynamic, trying to save you a few Watts of effect. Just look on the Scott Foil we reviewed last year. That frame would save you 10 Watts at 45 km/h compared to a standard frame. 10 Watts would for the average rider be about 5 % of your output, and these 5 % could make you go from a position outside top 10 in any race, to a podium place – maybe even a win.

But not many understands the physics behind aerodynamics, so I will try to help sorting this out, so you will understand how to become as slippery as an eal and gain some strength for the final sprint compared to the rest of the peloton. This can be done in just a very few equations, and does not demand much knowledge behind the theory. It is rather simple actually.

First off, there is the drag force, which is what we also can call the wind resistance. It is presented as:

This is the general equation we are using when speaking of the drag you are experiencing in the wind. The different factors in it are described below:

• - F_D is the force of drag. You will feel that force as the wind resistance. This force is measured in Newton [N].
• - ρ is the Greek letter of “Rho”. This is the density of the material you are in, which for us bike riders will be “air”. This value changes slightly with the        temperature. As the temperature rises, the value will be lowered, which means, that you will be quicker, with the same power output, on hot summer    days, compared to cold temperatures at Winter. – But lets come back to that. Below here is a table with the density of air at relevant different temperatures:
  
  
•  

Temperature (degree Celsius)	Density (ρ) (1 Atm) [kg/m3]
-10	1,341
0	1,292
5	1,269
10	1,246
15	1,225
20	1,204
25	1,184
30	1,164
35	1,145
40	1,127
45	1,109

• - V is the velocity you are travelling in. The velocity is measured in meters per second [m/s].
• - C_D is the drag coefficient. This factor is hard to find, unless you know the force of the drag you are experiencing, so there are a few static numbers we will be able to work with. These are in the table below.
• A is the frontal area of you and your bike. It is hard to measure this, so I have gathered a few numbers in the same table below along with the drag coefficient.

Bike position	Drag coefficient (CD)	Frontal area (A) [m2]
Upright on the bars/hoods	1,1	0,51
In the drops	0,9	0,36
In the drops while pacing	0,5	0,36

This drag force is what we want lowered in order to gain more speed with the same power output. As you can see, every time you double your speed, the wind resistance has increased 4 times. But there is more to it. The drag you are experiencing is not the power you need to put in the pedal. The power output needed is:

In this simple equation the three variables are:

• - Power. It is measured in Watt [W].
• - F_D is the drag force, which I mentioned before. It is measured in Newton [N] just like before.
• - V is the velocity. Still measured in meters per second [m/s].

What this equation really tells is, that if you want to find out what your power output needed is, is:

Suddenly it is V³, which means, that every time you double your speed, the necessary power output needed will need to be 8 times greater (!) if you want to

keep that speed up. The rolling resistance in the tires is also doubled, but that is nothing compared to the wind resistance you suddenly are experiencing.

Calculations of examples

Lets do some few experiments then. Lets imagine it’s a nice day with 20 degree Celsius, and you are riding with a speed of 30 km/h (8,33 m/s) on a day where there is absolutely no wind at all. How much would you gain by being in the drops instead of the hoods, and how much would pacing another rider in front of you help you?

Well, we will use equation number 3 to calculate this. It is actually just to put in the numbers. Rho can be found in the first table above. If you don’t know how to convert km/h to m/s, just divide by 3,6. If you want to go from m/s to km/h, multiply with 3,6.

When you have calculated it, you will have found out, that if you are having you hands in the hoods, you would have to put 195,4 Watts in the pedals. This is the power output needed just because of the wind resistance. Rolling resistance, loss in the bike, etc. will make this value greater, remember that. So in reality, doing 30 km/h demands more energy than 195 Watts.

If you are in the drops though, it would be just 112,9 Watts. You can see this by just changing the frontal area and the drag coefficient with values from the 2^nd table above. That is a total of 82,5 Watts saved, which means that the necessary power output of yours suddenly has decreased by a massive 42 %!

Lets try to see how much speed we will end up on, before we will experience the same power output needed in the drops, as when the hands are in the hoods. Here our variable would be the velocity (V), so equation 3 can be transferred to this:

If we put in the numbers, we will get, that the velocity you can achieve with the same power output in the drops as in the heads, will suddenly be 10 m/s, which is 36 km/h. So on paper you should now be able to ride 6 km/h faster by just changing the position of your hand! But remember, we aren’t taking notice of the other factors here. If they were calculated into this, they would eat up difference in your power output up faster, and you will only be able to gain 1-2 km/h by this change in reality. But that is still something that can make you a winner if you are in a break away.

If you are two or more riders in a breakaway riding in a line, you would be able to get even more speed for the same power. If you are pacing another guy you will suddenly find yourself only using 62,7 Watts to ride 30 km/h. That means that you will hit 195 Watts when you are riding 43,8 km/h!. So the drag of being in the hoods doing 30 km/h equals being in the drops, while pacing just a single rider in front of you, while doing almost 44 km/h! Of course the real value would be less due to the other factors. But between 35 and 40 km/h would be a good guess. That is why pacing is great and you can go faster and further in a group than alone.

Earlier I mentioned that the density of the air is changing with the temperature. Well, if you were riding in 10 degrees Celsius, with the hands placed in the hoods, you would need to have a power output of 202 Watts in order to maintain that speed. Compared to 20 degrees Celsius, you will suddenly need to put in 6,6 Watt more. That is an increase of 3,3 %. So if you want to make any new speed record, do it on the hottest day of the year if you want to lower your drag. But of course it will be a torture to do it in 30 degrees Celsius.

I hope you have understand the principle of drag better now, and that you can make your own calculations. It does make it more fun when you can use your own numbers and see how much power you had to put in the pedals in order to maintain a certain pace. Also, try to ride with the hands in hoods, and then do the exact same route with the hands in the drops afterwards. You probably will feel faster on the 2^nd run with the more aerodynamic position.

As for certain parts of the bike, I have already earlier written an article on why you should focus on buying good tires before spending money on wheels in order to become faster. You can read that article by clicking here.

All numbers above comes from fourth edition of “Thermal-Fluid Sciences” written by Yunus A. Cengel, John M. Cimbala, and Robert H. Turner. ISBN number is 978-007-132511-0.

Written by René

Read more: http://www.cyclingtipsonline.com/news/the-aerodynamics-of-a-bike-rider/