martedì 8 settembre 2015

CdA - Aerodynamic drag area estimation on the field

The author of this article is Mattia Michelusi. Decisions concerning use of the work, such as distribution, access, updates, and any use restrictions belong to the author.

Versione in italiano: CdA - Stima del coefficiente aerodinamico su campo

If you are riding on a flat road over 90% of the effort needed to maintain the speed is used to overcome air resistance (Fair). So, Fair is not the only factor (there is also rolling resistance and gravity resistance) but for sure it’s the most important:

Fair = 1/2 * Cda * P * s^2

Every factor of this formula is very important:

P - air density

In a previous article I have already talked about the importance of air density (Link: Record dell'ora e condizioni atmosferiche): a lower air density enables the cyclist to pedal faster for the same amount of power output due to the fewer air particles per square meter (the total air resistance to overcome is lower).

s - speed

Higher speed, higher air resistance. So, increasing your speed, the effort needed to overcome air resistance increases.

CdA - Drag area

CdA is the product of the drag coefficient of the system cyclist+bike and the frontal area (the portion of a body which can be seen by an observer placed exactly in front of cyclist):

CdA = Cd * A

Air density depends on the weather conditions, we can't artificially change them (unless you are in an indoor velodrome). If you want to go faster you need to keep an higher speed increasing the air resistance to overcome. So,  If you want to save energies or if you want to ride faster at the same power output, you just need to decrease your Drag Area (CdA). How can you do it? You can change your frame, your helmets, your clothing or your position on the bike. For sure the last one is the easiest and the cheapest.

The are many ways to measure CdA - drag area. The gold standard is wind tunnel testing where the wind is artificially generated from a fan on the cyclist-bicycle system. This technique is very sensitive to wheel type, yaw angle and cyclist position but it's very expensive and it doesn't simulate exactly the real conditions on the filed.

In order to simulate actual conditions, I chose a filed method called "Method of linear regression analysis" and I tried to measure my CdA on the field. This method consists of measuring mechanical power output using powermeter BePro (website: at different velocity to determinate the total resistive forces. According to the equation of cyclist's motion, the total resistive forces vary in a linear way with the square of the velocity. 

Average power as a function of average speed (hoods and drops position)
I found a flat road segment where I performed with my road bike five several trials at different velocities in hoods and drops position. For every step I recorded the average speed and power, and I estimated the air density considering the pressure, temperature and the realative humidity.

On the chart It's easy to see how keeping a drops position the output power is lower at the same speed than hoods position. It means that aerodynamic coefficient is better .

Anyway the purpose of this examination was to estimate my CdA, so with an algorithm I calculated the linear regression between total resistive forces and the  square of the velocity, estimating my CdA changing the position:

CdA hoods position: 0,363 m^2
CdA drops position: 0,314 m^2

So, keeping a drop positions my CdA decreased of about 13,5%.

What does this mean? 

It means that the final time to ride a 40km TT at 300 Watt with the same conditions (flat and straight road, no wind, same air density and Crr - Rolling Resistance) would be:

Hoods position: 1h 02' 42"
Drops position: 0h 59' 52"

The final time would be 2' 50" faster just changing the position.

I know that cycling is not just a mathematical algorithm, many factors can alterate the performance, but with this simple test it's easy to understand the importance and the advantages of keeping a more aerodynamic position.

The author of this article is Mattia Michelusi. Decisions concerning use of the work, such as distribution, access, updates, and any use restrictions belong to the author.

Dott. Mattia Michelusi

Capelli, C., Rosa, G., Butti, F., Ferretti, G., & Veicsteinas, A. (1993). Energy cost and efficiency of riding
aerodynamics bicycles. European Journal of Applied Physiology, 67, 144–149.
Capelli, C., Schena, F., Zamparo, P., Dal Monte, A., Faina, M., & di Prampero, P. E. (1998). Energetics of best
performances in track cycling. Medicine and Science in Sports and Exercise, 30, 614–624.
Di Prampero PE, Cortili G, Mognoni P, Saibene F. Equation of motion of a cyclist. J Appl Physiol. 1979 Jul; 47 (1): 201-6
Di Prampero P. E. La locomozione su terra, aria e acqua. Fatti e teorie. Edi-ermes Milano 1985
Di Prampero. Cycling on Earth, in space, on the Moon. Eur J Appl Physiol. 2000 Aug;82(5-6): 345-60
Martin, J. C., Milliken, D. L., Cobb, J. E., McFadden, K. L., & Coggan, A. R. (1998). Validation of a mathematical model for road cycling power. Journal of Applied Biomechanics, 14, 245–259.
Olds T.S., K.I. Norton, and N.P. Craig. Mathematical model of cycling performance. J. Appl. Physiol. 75 (2): 730-737, 1993

Nessun commento:

Posta un commento