Structural Dynamic Considerations in Wind Turbine Design - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 603

prototype design, there are some basic principles of scaling which apply to wind turbines,
and these are discussed in the following section.

Dimensional Scale Factors

Assuming that the rotor of the scaled wind turbine (scaled up or down) is to operate
at the same mean lift coefficient as its known predecessor, it can be expected that its loads
will follow all the basic aerodynamic and inertial scaling laws. Tip speeds will usually
remain constant for performance and acoustic noise reasons. If all dimensions of the
prototype are scaled in proportion to the diameter ratio D S / D P , where D S is the scaled
diameter and D P is the prototype diameter, other structural parameters would scale as
indicated in Table 10-1, to a first-order approximation.

Table 10-1. First-Order Scaling Relationships for HAWTs

Parameter Proportionality 1

Rotor speed

µ ( D S / D P ) -1

Blade centrifugal stress

µ ( D S / D P ) 0

Blade gravity-induced stress µ ( D S / D P ) 1

Blade centrifugal force µ ( D S / D P ) 2

Rotor power µ ( D S / D P ) 2

Rotor thrust µ ( D S / D P ) 2

Rotor torque µ ( D S / D P ) 3

System weight µ ( D S / D P ) 3

1 D s = scaled rotor diameter; D P = prototype rotor diameter

Use of Scaled Load Data from a Prototype Wind Turbine

In actual design practice it is found that the scaling of the parameters listed above will
vary somewhat from their first-order approximations. Weights do not grow as rapidly as
the cube law, but are proportional to about D 2.4 , because local departures from proportional
dimensioning are adopted. For example, a minor increase in the relative size of a blade
root will defeat the first-order rise of gravity-induced stress that would otherwise come with
an increase in diameter. Power and thrust, on the other hand, will change more rapidly than
indicated by the square law, because of the effects of tower height and wind shear. If due
consideration is given to the influence of scale on the frequency and amplitude of gusts
enveloping the rotor, it can also be expected that unsteady air loads will scale in proportion
to the steady air loads.
When the structural margins of safety in the prototype wind turbine are known to be
positive ( i.e. prototype design stresses are less than allowable stresses), the machine can be
scaled up or down moderately with little risk of miscalculation. This does not mean that
mere geometric scaling will be sufficient to insure that all margins of safety in the scaled
design will also be positive, but it does mean that the scaling influences upon loads and
stresses can be readily accounted for. Local design changes can then be made where
necessary without changing the overall prediction of the economic performance of the
scaled wind turbine system.