Contextual STEM Mathematical Modeling Using a Small Scale Savonius Wind Turbine for Public High School Education

Yayuk Badriatuz Zahroh, Nuryazid Muhibah, Moch. Kalam Mollah, Fairus Atika Redanto Putri, Zain Lillahulhaq

Abstract

This study develops a contextual STEM mathematical modeling framework using a small scale Savonius wind turbine as an engineering context for public high school education. The framework translates a fundamental renewable energy relationship into a structured sequence involving rotor geometry, wind energy, numerical calculation, ratio analysis, and graphical interpretation. A rotor diameter of 0.25 m and a height of 0.30 m were used, giving a swept area of 0.075 m². With an assumed air density of 1.225 kg/m³, available wind power was evaluated for wind velocities from 0.5-3.0 m/s using a cubic formula. The calculation results show that power increased from 0.0057 W to 1.2403 W across the modeled range. When the wind velocity is increased by factor of two, the available wind power increases by factor of eight. When the wind velocity increases by factor of three, the power rises by 27. The results show nonlinear behavior of the cubic function. The framework integrates science through wind energy, technology through the Savonius turbine, engineering through rotor geometry, and mathematics through functions, ratios, tables, and graphs. It is intended as a contextual mathematical modeling resource rather than an experimentally validated turbine performance model or a tested classroom intervention.

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References

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