This paper proposes the study of a tailsitter, delta-wing, convertible aircraft that combines the advantages of vertical take-off and landing (VTOL) and fixed-wing aircraft. Control during the transition between VTOL and horizontal flight, as well as the design of fault detection and isolation (FDI) algorithms should be considered to ensure safe operation. The main contribution of the paper is in the analysis of the flatness property of the convertible aircraft. Flat systems have the property that their inputs and states can be written as functions of a set of variables called flat outputs and their derivatives. Thus, an inverse dynamic model can be obtained which can be used to design path planning, nonlinear feedforward control, and FDI algorithms. First, the analysis of flatness in the horizontal flight is presented. Then, it is shown that this first set of flat outputs is singular at hover flight. However, this is only an apparent singularity as a second set of flat outputs can be obtained, which defines a chart of the aircraft’s dynamical model at hover and slow aerodynamic speed.