This study investigates the accuracy and robustness of degree-adaptive strategies for incompressible Navier–Stokes flows within the framework of the high-order hybridisable discontinuous Galerkin (HDG) method. A series of numerical experiments demonstrates that standard degree-adaptive procedures may fail to accurately capture key aerodynamic quantities of interest, most notably the drag. This deficiency is traced to the projection of solutions from higher- to lower-order polynomial spaces, which can violate the divergence-free condition of the velocity field. Owing to the strong coupling between velocity and pressure in incompressible flows, this violation leads to spurious pressure distributions in the wake, with a significant detrimental impact on drag predictions. To address this issue, a new conservative projection for the degree-adaptive process is proposed [1]. The performance of the standard adaptive strategy is compared with that of the enhanced approach incorporating the proposed projection for two transient flow problems involving the long-range propagation of vortical structures and gusts. The results show that the conservative projection effectively eliminates the numerical artefacts observed with the standard procedure, yielding stable and accurate drag estimates in close agreement with reference solutions. The proposed method incurs negligible additional computational cost, as it requires the solution of local element-by-element problems only in regions where the polynomial degree is reduced. [1] A Felipe, R Sevilla and O Hassan, A conservative degree adaptive HDG method for transient incompressible flows, Int. J. Numer. Methods Heat Fluid Flow 35 (1), 300-329, 2025.