At the Madeira River, north of Brazil, a natural phenomenon threatens the integrity and normal operation of an on-site hydroelectric power plant; thus, assemblies of containment structures, called logbooms, are installed across the river in order to protect the power plant installations. A truss-based nonlinear finite element method numerical tool is developed with the objective of designing and analyzing these assemblies. Initially, only the influence of the upstream velocity field is considered, and future modifications to account for the debris are expected. Code and solution verifications show that the tool converges reasonably well; the numerical error is about 0.2% of the theoretical value, and the uncertainty is about the same order: the results agree with analytical solutions from the simple catenary model. Finally, the method is validated by comparing numerical and experimental data; a satisfactory agreement is obtained, ascertaining the accuracy of the method: differences between experimental and numerical results are no higher than 6% and the trend of the tension force as a function of the free stream is followed by the numerical method.

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Many adaptations of the lifting-line theory have been developed since its conception to aid in preliminary aerodynamic wing design, but they typically fall into two main formulations, named $\alpha $ - and $\Gamma $ -formulation, which differ in terms of the control points chordwise location and the variable updated during the iterative scheme. This paper assess the advantages and drawbacks of both formulations through the implementation of the respective methods and application of standard verification and validation procedures. Verification showed that the $\Gamma $ -method poorly converges for wings with nonstraight quarter-chord lines, while the $\alpha $ -method presents adequate convergence rates and uncertainties for all geometries; it also showed that the $\Gamma $ -method agrees best with analytic results from the cassic lifting-line theory, indicating that it tends to overpredict wing lift. Validation and comparison to other modern lifting-line methods was done for similar geometries, and not only corroborated the poor converge and lift overprediction of the $\Gamma $ -method, but also showed that the $\alpha $ -method presented the closest results to experimental data for almost all cases tested, concluding that this formulation is typically superior regardless of the wing geometry. These results indicate that the implemented $\alpha $ -method has a greater potential for the extension of the lifting-line theory to more geometrically complex lifting surfaces other than fixed wings with straight quarter-chord lines and wakes constrained to the planform plane.