Page 365 - Wind Energy Handbook

ROTATIONAL SPEED 339

6.4.2 Influence of rotational speed on blade weight

The effect of rotational speed on blade weight can be explored with reference to
the family of blade designs just described. As in Section 6.3.1, it is assumed that the
blade design is governed by out-of-plane bending moments in fatigue and that the
moment fluctuations are proportional to the product of the wind speed fluctuation,
the rotational speed and the chord scaling factor (see Equation (5.25) in Section
5.7.5). By Equation (6.8) the chord scaling factor is inversely proportional to the
square of the rotational speed, so the moment fluctuations simply vary inversely as
the rotational speed.
The thickness to chord ratios at each radius are assumed to be unaffected by the
chord scaling, so the blade section modulus for out-of-plane bending at a given
radius is proportional to the product of the blade shell skin thickness, w(r), and the
square of the local chord. Thus

2
Z(r) / w(r)(c(r)) / w(r)=Ù 4 (6:9)
In order to maintain the fatigue stress ranges at the same level, we require the blade
section modulus, Z(r), to vary as the moment fluctuations, which, as shown above,
vary inversely as rotational speed. Thus

4
Z(r) / 1=Ù so w(r)=Ù / 1=Ù and w(r) / Ù 3 (6:10)
Blade weight is proportional to the skin thickness times chord, and thus varies as
rotational speed.

6.4.3 Optimum rotational speed

On the basis of the assumptions of Section 6.4.2 (which will by no means always
apply), blade weight increases in proportion to rotational speed. However, the
blade out-of-plane fatigue loads, which may govern the design of the nacelle
structure and tower, vary inversely as the rotational speed. It is therefore likely that,
as rotational speed is increased, there will be a trade-off between reducing costs of
the drive train, nacelle structure and tower on the one hand and increasing rotor
cost on the other, which will determine the optimum value.

6.4.4 Noise constraint on rotational speed

The aerodynamic noise generated by a wind turbine is approximately proportional
to the fifth power of the tip speed. It is therefore highly desirable to restrict turbine
rotational speed, especially when the wind speed – and therefore ambient noise
levels – are low. Consequently manufacturers of turbines to be deployed at normal
sites on land generally limit the tip speed to about 65 m/s. Experience suggests that
this results in wind turbine noise levels on a par with ambient levels at a distance of
400 m, which is the normal minimum spacing between turbines and habitations.