A series of design models for the quad-rotor vehicle (QRV) are presented. These design models include a full nonlinear model which contains the most relevant dynamics. This model uses a traditional aeronautical structure. This structure may not be the best for typical nonlinear control design, but it is useful for simulation and aeronautical variables evaluation. A second nonlinear model, shown to be equivalent to the previous one, is derived. This model complies with the typical state space structure used for most nonlinear control design methods. Therefore, by using this model it is possible to simplify the controller design task. A disadvantage is that both models are represented by a set of highly nonlinear differential equations and may complicate the design of simple control laws. Therefore, a simplified model which is almost linear is derived. This model is based on a linear approximation of the main QRV dynamics plus a simple nonlinear term arising due to the yaw motion. Through an extensive set of simulations, the operating range of the approximate model is elucidated. It is shown that this model is adequate for linear controller design for a very wide range of operation.