# The Impact of Skinsuit Zigzag Tape Turbulators on Speed Skating Performance
## 2 The Flow over the Lower Legs  
The flow over bluff objects with rounded edges is typified by the Reynolds number. It describes the ratio of the inertia forces (in terms of flow speed V, characteristic length L and density \(\rho\)) over the viscous forces (in terms of the dynamic viscosity \(\upmu\)) in the flow:  
\[\text{Re}=\frac{\rho.\text{V.L}}{\upmu} \tag{1}\]  
For cylinders and spheres, the characteristic length is the diameter, D. The Re-number is closely related to the laminar-to-turbulent transition location of the boundary layer flow along the surface of an object and the resulting drag. Transition is a delicate process, which is not only influenced by the shape of the object and its orientation towards the incoming flow, but also by its surface roughness and by disturbances in the flow, such as free-stream turbulence. For bluff bodies, such as cylinders and spheres, there is a significant drag reduction (the \"drag crisis\") at a certain Re-number, called the critical Reynolds number, due to the boundary layer flow becoming turbulent before separation, which leads to a smaller drag and a higher wake static pressure, compared to a situation with laminar separation. For lower (sub-critical) Reynolds numbers, the flow is mostly laminar. Although a laminar boundary layer has a lower friction drag than a turbulent layer, it has the disadvantage of losing its momentum close to the wall of the object relatively fast, resulting in separation of the flow from the object, even prior to reaching the thickest point. This leads to a large wake with a low pressure, which, combined with the stagnation pressure at the leading edge of the object, results in a high pressure drag.  
It is long known that this pressure drag of circular cylinders in the sub-critical Reynolds number regime can be significantly reduced by tripping the laminar boundary layer, forcing it to become turbulent [9; 10], thus adding momentum to the lower part of the boundary layer, helping it to flow against the strong adverse pressure gradient at the back of the cylinder, which postpones the separation of the boundary layer, increases the static pressure in the wake and reduces the size of the wake.  
The measurements of the effect of trip wires on the drag of a model leg presented in Reference [4] showed strong resemblance with the flow around a two-dimensional cylinder. Although the cross-section varies and the drag values are different, the flow mechanisms are quite comparable.  
The impact of zigzag tape on the flow around a leg is presented in Figure 2, using the fluorescent-oil-flow visualization technique. The pictures were taken in the Delft University  
Figure 1: The foam zigzag tape for the lower legs and cap introduced at the 1998 Nagano Olympics.  
1.25 \(\times\) 1.80 m, of low-speed low-turbulence wind tunnel (LTT), using the same mannequin leg as in Reference [4]. The flow over the leg was visualized with a UV lamp. In the left picture, the light yellow band shows a laminar separation bubble, following a laminar region and the subsequent turbulent separation with reversed flow. Darker areas point at a higher surface shear stress, which transports the oil in flow direction. In the right picture, clearly the small tape-induced vortices can be seen, which make the flow turbulent and move the separation location more backwards, reducing the pressure drag.