Modelling ice throw trajectories from wind turbines

Abstract

Wind turbines in cold climates can occasionally experience ice throws that travel significant distances, posing a low-probability but high-consequence safety risk. Current guidelines typically rely on the empirical Seifert safety distance, defined as d = k x (H + D), where k is the throw factor – commonly set to 1.5, H is the hub height, and D is the rotor diameter. However, both observational field data and modelling studies suggest that this formula may be overly conservative and tends to overestimate actual throw distances.

Observational data were compared against the Seifert safety distance. The furthest recorded ice throw corresponds to a throw factor of 1.02 so that; d = 1.02 x (H + D), indicating that ice fragments do not travel as far as the standard safety margin with k = 1.5 suggests.

A Monte Carlo trajectory model was developed, which was solved numerically by integrating the equations of motion, including gravity, drag, and lift forces. Hourly wind and icing conditions at Blakliden Fäbodberget were extracted from the New European Wind Atlas, filtering for periods with positive ice accretion on a standard 100 m cylinder. Fragment properties were drawn from the ICETHROWER database. Sensitivity analyses reveal that turbine geometry (hub height and radial release position) exerts only a minor influence on throw distance. In contrast, fragment mass, projected cross-sectional area, wind speed, and ejection angle primary determines the fragments throw distance.

Models that include lift tend to overestimate the maximum throw distance by twice of the observed maximum, and also fails to capture the steep decline in throw probability after certain ranges. In contrast, the drag and gravity model also overestimate throw distances, but by a smaller margins.

Despite this, the model can be applied to generate realistic exclusion zones within a wind park during icing conditions, offering physics-based safety zones compared to the fixed-radius safety guidelines.