Two low-order, parametric models are developed for the forces and moments that a rotating propeller undergoes in forward flight. The models are derived using a first-principles-based approach, and are computationally efficient in the sense of being represented by explicit expressions. The parameters for the models can be identified either using supervised learning/grey-box fitting from labelled data, or can be predicted using only the static load coefficients (i.e., the hover thrust and torque coefficients). The second model is a multinomial model that is derived by means of a Taylor series expansion of the first model, and can be viewed as a lower-order lumped parameter model. The models and parameter generation methods are experimentally tested against 19 propellers tested in a wind tunnel under oblique flow conditions, for which the data is made available. The models are tested against 181 additional propellers from existing datasets.