# Cycling Aerodynamics

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 later. Below here is a table with the density of air at relevant different temperatures:

Temperature (degree Celsius) |
Density (ρ) (1 Atm) [kg/m |

-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 (C |
Frontal area (A) [m |

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 V^{3}, 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

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bike | rider | aerodynamic | aerodynamics | drag | wind | resistance | how to | calculate | example | examples | riding | speed | calculations