This article presents the dynamical modelling of a novel active aeroelastic structure. The adaptive torsion wing concept is a thin-wall, two-spar wingbox whose torsional stiffness can be adjusted by translating the spar webs in the chordwise direction inward and towards each other using internal actuators. The reduction in torsional stiffness allows external aerodynamic loads to induce twist on the structure and maintain its deformed shape. Here, the adaptive torsion wing system is considered as integrated within the wing of a representative unmanned aerial vehicle to replace conventional ailerons and provide roll control. The adaptive torsion wing is modelled as a two-dimensional equivalent aerofoil using bending and torsion shape functions to express the equations of motion in terms of the twist angle and plunge displacement at the wingtip. The full equations of motion for the adaptive torsion wing equivalent aerofoil were derived using Lagrangian mechanics. The aerodynamic lift and moment acting on the aerofoil were modelled using Theodorsen's unsteady aerodynamic theory. A low-dimensional, state-space representation of an empirical Theodorsen's transfer function was adopted to allow time-domain analyses. Four actuation strategies were investigated. Figures of merit, including plunge displacement, twist angle, actuation forces and actuation powers, were quantified and discussed for each of the scenarios. This study allows the conceptual design and sizing of the internal actuators that are required to drive the webs.