# The Impact of Skinsuit Zigzag Tape Turbulators on Speed Skating Performance
## 5 The Impact of the Zigzag Strips on Skating Performance in a Real Skating Environment
### Looking Closer at the 1998 Nagano Results  
The first analysis is based on three consecutive 5000 m events in 3.5 months' time, just before, at and just after the 1998 Nagano Olympic games in which Dutchman [PERSON] came out as a winner. Since these were all world records, this enables us to compare his performance in the three races, assuming he constantly used his average optimum power. To investigate this in more detail, let us look at the three races, starting in Heerenveen, the Netherlands (Thialf venue), during a world cup meeting on 7 December 1997 (without drag reducing zigzag strips) and ending in Calgary, Canada (Olympic Oval), during the World Championships Single Distances on 27 March 1998, where all the top 10 skaters used the zigzag strips. To determine how much power a skater puts in his propulsion, generally, a simple Equation (3) can be used:  
\[\mathrm{P_{req}}=\frac{1}{2}\rho\mathrm{V^{3}C_{D}A+\mu mgV} \tag{3}\]  
It combines the average power required to overcome the aerodynamic drag force of the skater, in which \(C_{D}\) is the average drag coefficient, A is the frontal area and \(\rho\) is the local air density, and the average ice friction force with \(\mu\), the ice friction coefficient; m, the mass of the skater; and g, the gravitational acceleration. For momentary velocities, eq. 3 is not suited, since a term covering the accelerations is omitted. To calculate [PERSON]'s average required power, a value of 0.275 for the drag area \(C_{D}A\) was used following from the equations suggested by [PERSON] [13], with a correction on the basis of the open jet measurements reported above. The skater's mass and length were taken to be 85 kg and 1.90 m [14]. References [1, 15] give a variety of values for the ice-friction coefficient. Reference 1 mentions a value of present day friction coefficients in ice rinks as low as 0.0025. To account for developments in blade material and thickness and experience in ice preparation since 1997, the friction coefficient was set at 0.004. Table 3 presents the calculated required power for the two extremes in density: Heerenveen and Calgary, on the basis of the parameters mentioned above, so without accounting for drag reducing devices in Calgary. The barometric pressures were taken from historic weather data of stations near the venues [16] (Leeuwarden air base at 38 km distance, sea level, and Calgary International Airport at 18 km distance, altitude 1099 m) around the time of the day the races were held. With the local pressure and temperature given, the densities were calculated for the respective elevations (0 and 1034 m). As there is no public record of the temperatures in Thialf and the Olympic Oval, they were taken equal to the one measured during the Nagano race given in the official report published by the Nagano Winter Games organizing committee [17]. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Location** & **T** (\({}^{\circ}\)**C) & **Pbar (hPa)** & \(\rho\) (kg/m\({}^{3}\)) & \(\mu\) & **g (m/s\({}^{2}\))** & **Time** & **C\({}_{D}\)A** & **V\({}_{avg}\) (m/s)** & **P\({}_{req}\) (W)** \\ \hline Heerenveen & 13 & 1012 & 1.232 & 0.004 & 9.806 & 6:30.63 & 0.275 & 12.800 & 398 \\ Calgary & 13 & 890 ** & 1.084 & 0.004 & 9.804 & 6:21.49 & 0.275 * & 13.107 & 379 \\ \hline \hline \end{tabular}  
* \({}^{*}\) Without drag-reducing devices, ** including 7 hPa for 65 m height difference airport ice rink.  
\end{table} 
Table 3: Calculation of Romme’s average power output in Heerenveen 1997 and Calgary 1998. One would expect that, with a power available of 398 Watts in Heerenveen, the speed in Calgary due to the substantially lower air density would be much higher (13.335 m/s, according to Equation (1)). However, the average speed of 13.107 m/s requires an estimated power of only 379 Watts, with an unchanged drag area, the power for a configuration with an assumed decreased drag due to zigzag strips even being lower.