Introduction to Wind Turbine Technology - Small Wind Turbines: Analysis, Design, and Application - page 13

Table 1.2 Properties of the
international standard
atmosphere

Altitude (m) T (C) q (kg/m 3 ) m (m 2 /s)
0 15 1.225 1.46 9 10 -5
1,000 8.5 1.112 1.58 9 10 -5
2,000 2.0 1.007 1.71 9 10 -5
3,000 -4.5 0.909 1.86 9 10 -5
4,000 -11.0 0.819 2.03 9 10 -5
5,000 -17.5 0.738 2.21 9 10 -5
6,000 -24.0 0.606 2.42 9 10 -5
The ISA is available in the Matlab Aerospace blockset and is
easily obtained on the internet, e.g. http://www.aero-

spaceweb.org/design/scripts/atmosphere/

danger is that if the wind speed is high enough, the centrifugal forces within the
blades will shatter them. The well-known video clip of a large wind turbine blade
shattering, one of the remaining blades then hitting the tower, which buckled and
collapsed, is a graphic demonstration of over-speeding. 3 Another example will be
discussed in Chap. 12 . Figure 1.6 shows why the current trend for both large and
small turbines is to attempt to keep a constant k as the wind speed varies. This is a
major challenge for small turbines where the wind speed is not measured. The
control strategy to achieve constant-k operation is an implementation of what is
usually called ''maximum power point tracking'', MPPT. It is explained further in
Chap. 12 .
The C P values for the Bergey 10 kW turbine are much lower than for the larger
machine. This is due partly to the use of a constant chord, untwisted blade, chosen
presumably on the grounds of cost and ease of manufacture, and also to the lower
Reynolds numbers which reduces the lift to drag ratio of the blade sections which
reduces the torque and hence power, as will be made clear in Chap. 4 (Table 1.2 ).

Example 1.3 It is proposed to install a remote area power system in a village in
Tibet at an altitude of just over 5,000 m. As the RAPS contains a wind turbine, it is
necessary to estimate the reduction in power caused by the increase in altitude.

Answer From the material presented in this chapter, it is reasonable to expect that
C P should remain roughly constant as the altitude varies. Thus the change in power
occurs through the change in density, much like that shown in Table 1.1 and
Fig. 1.6 . One way to estimate the density change is from the ''International
Standard Atmosphere'' (ISA) which is often used to account for altitude effects on
aircraft performance. Table 1.3 gives the low-altitude ISA variation of tempera-
ture, density, and kinematic viscosity with altitude.
The ISA gives the sea-level density of air as 1.225 kg/m 3 (and the temperature
as 15) and the density at 5,000 m as 0.738 kg/m 3 . Thus the power reduction

3 The author first saw this video clip on Youtube. Typing ''wind turbine destruction'' into a
search engine should find it.