Predicting critical velocities in telescopic wind turbines: the role of resistive mass and radius control

The invention of telescopic blade technology marks a significant step in wind turbine innovation by enabling dynamic adjustment of blade radius in response to changing wind conditions. Since its proof of concept in 2002, radius control has relied on data from conventional fixed-blade turbines, requiring costly prototype fabrication at the initial step in every new telescopic blade design. The dependency on fixed-blade data presents a gap in cost-effective design strategies. This study proposes an alternative analytical framework that eliminates the need for preliminary fixed-blade prototypes. The method introduces an alternative radius adjustment function and investigates the role of turbine resistive mass in determining critical velocity points. Two theoretical models are developed: a rotating lever model, which conceptualizes the turbine as a lever machine comparing effective wind force against resistive load, and a wheel–axle model, which examines the effective cross-sectional interaction between wind particles and the rotor. The findings indicate that the models can reliably predict critical operational velocities (cut-in, rated, and cut-out) without the need for extensive field trials. By deriving analytical relationships between turbine design parameters and velocity thresholds, the models provide a low-cost, generalizable approach to telescopic blade design. The results demonstrate that optimal generator performance is achieved when the rated angular velocity of the turbine aligns with the site’s average wind speed. The broader implication of this work is a cost-efficient pathway for developing site-specific telescopic turbines, offering design simulation and performance optimization prior to fabrication.