The importance of aerodynamics in cycling cannot be underestimated. In professional cycling speeds above 40 km/h are the norm. In time trial (TT) average speeds above 50 km/h are common. At 40 km/h 85% of the power of the cyclist used to combat the aerodynamic resistance, also known as drag. Rolling and mechanical resistance only accounts for 15%. At 50 km/h aerodynamic drag accounts for 90% of total power.

It must be clear that most potential in increasing a cyclists speed must be found in optimizing aerodynamic drag. The suits, shoes, bikes and helmets of a cyclist are already optimized for aerodynamic drag. The exposed skin is there for a potentially interesting area for aerodynamic optimization.

**I . THE SCIENCE BEHIND AERODYNAMICS IN CYCLING **

Aerodynamic drag [1]: As you cycle through the air, your bike and body need to push the air around you, This creates higher pressure in front of you and lower pressure behind you. Because of this, the air exerts a net force against you as you ride. There are a few things that dictate how much force the air exerts against you. The faster you ride, velocity V (m/s), the more force the air pushes and pulls you back. You and your bike present a certain frontal area A (m2) to the air. The larger this frontal area, the more air you have to displace, and the larger the force the air pushes against you. This is why cyclists and bike manufacturers try hard to minimize frontal area in an aerodynamic position. The air density Rho (kg/m3) is also important; the more dense the air, the more force it exerts on you.

Finally, there are other effects, like the smoothness of your clothing and the degree to which air flows laminarly rather than turbulently around you and your bike. Optimizing your aerodynamic positions also help with this. These other effects are captured in a dimensionless parameter called the drag coefficient, or Cd.

The formula for the aerodynamic drag acting on a cyclist, in metric units, is:

F (N) = 0.5 · Cd · A · Rho · V2

With A the frontal surface area of the cyclist in m², Rho the density of the air in kg/m³, V the speed of the cyclist in m/s and Cd the drag coefficient. The power Pcyclist (Watt) that must be provided to your bicycles wheels to overcome the total resistive force Fresist (N) while moving forward at velocity V is:

P = F · V

with

F (N) = F + F + F . .

Fdrag is by far the dominant force in this equation. To give an example: For a typical rider of 70kg, with a bike weighing 7kg, a frontal area A of 0,0509m², a drag coefficient Cd of 0,63, on a 0% slope, with normal air density, and a cycling speed op 50km/h, we get: Fdrag= 38N (527 Watt), Frolling= 3,8N (53 W). Or stated differently at 50km/h, for a cyclist in normal position and conditions, almost 90% of the power he/she is producing goes to overcoming the air resistance.

**I I . AEROSPEED GEL CONCEPT**

The NAQI Aero Speed Gel concept works similarly as the dimples in a golf ball. By roughening the surface of a round object, turbulence can be increased in the boundary layer. This increased turbulence causes the flow to become more resistant against separation. This resistance to separation makes the flow stick to the surface longer and thereby creating a smaller wake behind the object. This smaller wake translates into a smaller area of lower pressure behind the object and thus lower aerodynamic drag.

By adding vortex generators to a gel, that is applied to arms and/or legs of a cyclist, these special particles aid in the generation of turbulence in the boundary layers and therefor the postponement of flow separation behind the arms and/or legs of the cyclist. Figure 2 show the flow separation around a spherical object with two different separation points, marked by the red arrows.

To see the effect of the air speed on the turbulence, it was chosen to test a four different air velocities, all correlated to relevant cycling speeds. Chosen wind tunnel air velocities: 10.4, 11.8, 13.3 and 14.8 m/s. This corresponds with cycling speeds of 37.5, 42.5, 47.9 and 53.3 km/h. Measured drag force on the cylinder were converted to watt for easier comparison.

Each measurement was repeated four times. Two times with a measurement time of 30 seconds, and two times with a measurement of 60 seconds. This was done to check the repeatability of the test setup. The difference between the four measurements was always below 0.1 N, which proves that the repeatability was excellent.

**I I I. AEROSPEED GEL MEASURMENT PHASE 1**

All aerodynamic drag testing was done in the state-of-the-art low speed wind tunnel testing facility at Bike Valley. Initial testing of the first prototypes was done on a cylinder wrapped with pig-skin. Second phase of testing was done on real cyclists

*Setup 1, Aero Speed Gel on pig-skin*

To test a reference object that simulates a leg or arm of a cyclist, a cylinder was chosen with a diameter of 100mm. This cylinder was wrapped with the skin of a pig, because this closely resembles human skin. The goal of this test protocol was to optimize the carrier liquid and vortex generator inside the liquid.

*Measurement results*

In figure 4 we can clearly see that all NAQI Aero Speed Gel prototypes already gave an improvement relative to the untreated baseline (light blue). The best performing vortex generators were chosen for the next phase of testing.

**I V. IMPROVEMENT AEROSPEED GEL MEASURMENT PHASE 1**

*A. Setup Aero Speed Gel testing on real athletes*

Second phase of testing was with real cyclists. It was chosen to test with a cyclist in TT position and clothing, with standard clothing a position for normal road cycling and with a triathlon suite on a triathlon bike. 5 athletes were used as test subjects. It was also chosen to test the gel on both the arms and the legs, depending on the specific clothing and discipline (TT, road, triathlon). For this testing phase it was chosen to only test at one air speed. The choses air speed chosen to be relevant for the specific discipline. The chosen air speed was 13.9 m/s or 50.0 km/h for TT position, 12.4m/s or 44.64 km/h for standard cycling position and 10.9m/s or 39.2 km/h for triathlon

Because the position of the cyclist with different gels and without the gel has to been exactly the same, the repeatability was also checked by doing every measurement twice. Within a range of about 1.5 watt, the results correlated well. The position of the cyclist was checked and adjusted for every measurement to be exactly the same, by plotting the contours of the position of the reference measurements in front of the cyclist. This way he/she could check and adjust his/her position to exactly match that of the reference. See also Figure 5.

*B. Measurement results*

In TT position the average drag was 374.5 Watt, without NAQI aero speed gel and with gel the drag was 360.5 Watt. This gives a difference of 14 Watt at the chosen speed. Which corresponds with an reduction in drag close to 4%. The gain in time on a 9 km TT using this NAQI aero speed gel is 8.4 seconds or 46.6 seconds on a 50 km TT. Thus close to 1 second per km. This result was obtained by only applying NAQI Aero Speed Gel to the legs of the cyclist.

Similar tests were done on a triathlete and road cyclist in normal position and clothing. For the triathlete the average baseline drag was 235.5 watt. The drag with NAQI Aero Speed Gel on the arm/ shoulder and legs was 222 watt. It might seem contradictory that applying the gel to both arms and legs instead of just legs, does not give rise to an extra reduction of drag. But remember that for the triathlete the testing was done at 39km/h instead of 50km/h.

The average reduction in drag was 13.5 watt. This leads to a time saving of 307 seconds on the iron man distance. Or a reduction in drag of almost 6%.

For the standard road racing position and clothing baseline drag was 420.7 watt at 44.6 km/h. With the NAQI aero speed gel on the legs the drag was reduced to 405.2 watt. Which again leads to a drag reduction of almost 4%.

**V . CONCLUSION**

*The NAQI*® *Aero Speed Gel uses vortex generators to enhance the turbulence in the boundary layer of the air flow across certain parts of a cyclist. This enhanced turbulences leads to later flow separation and a corresponding smaller wake and lower drag. *

*Extensive wind tunnel testing showed a drag reduction of almost 4% when used on only the legs of a cyclist. When also applied to the shoulder and arms of a triathlete a reduction in drag of almost 6% was obtainable. *

* *

*REFERENCES *

[*1] Fage, A. & Warsap, J. H. (1930), The effect of turbulence and surface roughness on the drag of a circular cylinder. Aero. Res. Com. London, R. & M. no. 1283. *

*[2] Singh, S. P. and Mittal, S. (2005), Flow past a cylinder: shear layer instability and drag crisis. Int. J. Numer. Meth. Fluids, 47: 75-98. doi:10.1002/fld.807 *

*[3] Alam, Firoz & Chowdhury, Harun & Moria, Hazim & Mazumdar, Himani & Subic, Aleksandar. (2010). An experimental study of golf ball aerodynamics. 1-4. Proceedings of the 13th Asian Congress of Fluid Mechanics 17-21 December 2010, Dhaka, Bangladesh *

*[4] Drag of a sphere, NASA, https://www.grc.nasa.gov/www/K-12/airplane/dragsphere.html *

*[5] zgoren, Muammer & Dogan, Sercan & Okbaz, Abdulkerim & Sahin, Besir & Akilli, Huseyin. (2011). Investigation of surface roughness on the flow structure around a shere. Ankara international aerospace conference. September 2011 *

*[6] Achenbach, E. (1971). Influence of surface roughness on the cross-flow around a circular cylinder. Journal of Fluid Mechanics, 46(2), 321-335. *

*[7] Crouch, Timothy N.; Burton, David; LaBry, Zach A. and Blair, Kim B. “Riding Against the Wind: a Review of Competition Cycling Aerodynamics.” Sports Engineering (May 2017). *

*AUTHORS *

*First Author *– Nikolaas Van Riet, cycling aerodynamics consultant, former head of the wind tunnel testing facility at Bike Valley, N ikolaas.vanriet@gmail.com

*Second Author *– Greet Claes, Head of research & development at NAQI, G.Claes@naqi.com