Recently, several insect-and hummingbird-inspired tailless flapping wing robots have been introduced. However, their flight dynamics, which are likely to be similar to that of their biological counterparts, remain yet to be fully understood. We propose a minimal dynamic model that is not only validated with experimental data, but also able to predict the consequences of various important design changes. Specifically, the model captures the flapping-cycle-averaged longitudinal dynamics, considering the main aerodynamic effects. We validated the model with flight data captured with a tailless flapping wing robot, the DelFly Nimble, for air speeds from nearhover flight up to 3.5 m/s. Moreover, the model succeeds in predicting the effects of changes to the center of mass location, and to the control system gains. Hence, the model is suitable even for the initial control design phase. To demonstrate this, we have used the simulation model to tune the robot's control system for higher speeds. Using the new control parameters on the real robot improved its maximal stable speed from 4 m/s to 7 m/s.