**Nomenclature**

nuances even for large amplitude (45°) at the ramp-up regime and partially at the ramp-hold only. At ramp-down regime, the UVLM results deviate from the exper-

**Figures 12** and **13** show the Shedding of trailing vortices and wake convection shape downstream for 25° and 45° amplitudes ramp maneuvers. All the figures show the same convection pattern for the three pivot locations with an increase in

In this chapter, different classical analytical models were presented in a simple mathematical form based on potential flow to solve unsteady problems constrained by an input motion. A canonical pitch ramp motion is chosen to present the input motion for two different ramp amplitudes (25° and 45°) and three pivot location on the airfoil chord (*c=*4,*c=*2, 3*c=*4). The analytical results were compared to the experimental data and the comparison revealed an acceptable agreement at the pitch ramp amplitude of 25*<sup>o</sup>* compared to the results presented by the 45*<sup>o</sup>* ramp amplitude case. Thus, those models can be considered as promising aerodynamic models for predicting lift coefficient for such manoeuver at a ramp amplitude up to 25*<sup>o</sup>* only. Along the four analytical models, the UVLM showed very good results for the two ramp amplitude cases. It should be noted that, the UVLM captures all geometric nonlinearities, wake deformation, rolling wake, leading edge suction and post stall without the inclusion of leading edge vortex effects. Duhamel and the state space models appear to have the same behavior which asserts that the state space model shares the same physical base and

**Table 2** discuses and concludes the output of each proposed model with the perspective of output response, pitch amplitudes, computational cost and the

The benefits of the UVLM compared to other methods is that is enabling aerodynamic modeling for arbitrary motion. An extension is easy to implement to include a formulation of the boundary conditions for arbitrary three-dimensional motion and control surface rotation. Furthermore the calculation of unsteady induced drag by a nonlinear extension of the force computation can be done. Furthermore the proposed UVLM method shows advantages in predicting unsteady aerodynamic forces of high frequency motion compared to other analytical models. In general, it can be said that the unsteady vortex lattice method is a powerful tool for modeling of incompressible and inviscid unsteady aerodynamics. A continuous time formulation in particular can be used to decrease the computational costs for aeroelastic simulations. The possibility of calculating unsteady loads without the need of approximations for time-domain simulation makes the method especially useful within aeroservoelastic optimization algorithms. Other models formulated in

**Models Response type Large amplitude Computational cost Loads** Theodorsen Steady state harmonic force Wagner Transient Force State space Full response Force UVLM Full response √ √ Pressure

imental results and appeared to be over predicted.

**5. Conclusion**

*Biomimetics*

obtained loads.

**Table 2.**

**118**

the y axis vortex location with increasing the ramp amplitude.

obtained the same results compared to Theodorsen's model.

*Proposed models output parameters for solving pitching maneuvers.*

