Aerofoils: Lift, Drag, and Circulation - Small Wind Turbines: Analysis, Design, and Application - page 64

because the centrifugal loads on a blade get larger as rated power decreases, see
Table 1.7 . In other words, it desirable for structural reasons to use thick aerofoil
sections near the hub of small turbines, but this would lead to poor aerodynamic
performance. Furthermore, Chap. 6 demonstrates that the hub region is especially
important in generating the starting torque at low wind speed.

4.4 Aerofoil Lift and Drag at High Angles of Attack

Particularly at low Re, there is little lift and drag data for high angles of attack, but it
is often the case that the twist of a well-designed horizontal-axis blade is close to 0
at the tip. When the blade is stationary its tip a is nearly 90 so that performance at
high a is important for the analysis of starting behaviour in Chap. 6 . Sheldahl and
Klimas [ 7 ] measured the lift and drag of the NACA 0012 and NACA 0015 at high a
as did [ 8 ] for the NACA 0012 and [ 9 ] for a number of NACA four digit aerofoils, of
which the 4415 and 4418 are given here. Also shown are the lowest turbulence
results for the 21% thick NACA 65 4 -421 section from Devinant et al. [ 10 ]. At their
maximum turbulence level of 16%, the high-a lift did not change significantly from
that shown but the maximum C d increased to 2.2. The data for Re [ 2 9 10 5 are
collected in Fig. 4.5 and the data sources are listed in Table 4.2 . Figure 4.6 has
results for lower Re with the sources listed in Table 4.3 . Low Re data comes
from [ 11 ] for the NACA 0012 and [ 5 ] for the MEL 081 a 14% thick section
specially designed for small wind turbines. At high a any reasonably thin aerofoil of
small camber should behave more or less as a two-dimensional, thin flat plat
held normally to the flow for which C l & 0 and C d & 2. Therefore, the flat plate
data [ 12 ] 2

are included. Also shown in the figures are the two equations

C l ¼ A sin 2a ð 4 : 6 Þ

and

C d ¼ B C cos 2a ð 4 : 7 Þ

where A, B, and C can be Re and aerofoil dependent [ 13 ]. Figures 4.5 and 4.6 show
Eqs. 4.6 and 4.7 respectively with typical values of A = B = C = 1. As an aside,
the flat plate is an obvious counter-example to the simple-minded but surprisingly
common explanation of aerofoil lift purely as a consequence of Bernoulli's
equation and the supposed fact that the air must speed up as it flows over the upper
part of the section. There can be no speeding up over a thin flat plate.
There is more scatter in the low-Re data and the apparent trend of decreasing C l
and C d as Re decreases is not consistent. More data is urgently needed.

2 The data is taken from Table X of the paper. In the appendix the authors suggest that the results
for a = 908 should be reduced by 13.5% and those at 30 by 8% to account for wind tunnel
blockage. The correction at other angles was found by linear interpolation.