*6.2. Lift Coe*ffi*cient 0.4*

For the case with lift, thin and thick sections have surprisingly equal drag. Exceptions are sections with a short trailing edge at medium and high Reynolds numbers where the thick sections have higher drag. As can be seen in Figure 14, the thin section does not exhibit separation, but the thick section separates at the trailing edge. The separation is on the pressure side of the airfoil; this phenomenon will be explained in more detail below.

**Figure 14.** Velocity plot and pressure plot of thin (**left**) and thick (**right**) sections.

Generally, sections with long leading and trailing edges are the best, while sections with short leading and trailing edges are the worst. The performance of other combinations depends on the Reynolds number. As can be seen in Figures 15 and 16, an interesting phenomenon occurs. For the shape with short trailing edge, there is large steady separation on the pressure side of the section. This is due to the laminar flow over the pressure side, as the plot of the friction coefficient shows in Figure 15. On the suction side, the boundary layer is turbulent, and, as explained above, the turbulent boundary layer is much more resistant to separation.

**Figure 15.** Velocity plot and skin friction coefficient of short leading edge and long trailing edge (**left**) and long leading edge and short trailing edge (**right**) sections.

The asymmetric separation causes an interesting flap effect, as seen in Figure 16 Here the streamlines are shown for the short trailing edge. This asymmetry increases the lift of the section.

The trailing edge angle has a very small effect on the drag, as can be seen in Figure 17, where five different trailing edges are compared.

**Figure 16.** Streamlines of long leading edge and short trailing edge section.

**Figure 17.** Five different trailing edge angles are compared, *x*-axis nose radius, *y*-axis drag coefficient times 103.

Apparently, a rather small (but not too small) leading edge radius is the best for the thin sections. The same is true for the thick sections, however with one exception at high Reynolds number and short leading edge. This result can be related to the different ways the outline of the section approaches the maximum thickness. For the short leading edge, the thickness increases faster, since there is less space to reach the zone with constant thickness. On the other hand, with the long leading edge length, the nose radius gets too small. As can be seen in Figure 18, the section with a long leading edge has a thicker boundary layer, resulting in a larger drag coefficient. The thicker boundary layer is caused by the earlier transition, which is very close to the nose for this section.

The thin parallel-sided sections at the smallest Reynolds number are better than the NACA sections by about 10%. For the intermediate and high Reynolds number, they are about equal. The thick sections have, on average, 35% higher drag than the NACA sections. Especially at low Reynolds number (300,000) and for thin sections, some parallel-sided profiles perform better than NACA0004 profile. The nose radius of the NACA0004 is very close to R4, so this effect cannot be related to the nose radius. One cause of this behavior can be the length of the leading edge, since the two best shapes have the short leading edge length and the NACA profile has the longest leading edge. The main contribution to the drag coefficient for the NACA section is the pressure and not the friction. These results confirm the conclusion made by Pollok (1987), who affirms "There are many situations where parallel-sided aerofoil sections with leading and trailing edge fairings of limited chord wise extent have advantages over conventional sections."

**Figure 18.** Velocity plot and pressure plot of short leading edge (**left**) and long leading edge (**right**) sections.
