We experimentally investigate the propulsive characteristics of a pitching NACA 0012 airfoil section, with emphasis on thrust and propulsive efficiency, at a Reynolds number of $1.7\times {10}^4$. For the sake of mechanical simplicity, we consider an airfoil restricted to a single actuator in the pitching direction. We examine the effect of changing the airfoil's axis of rotation, finding that contrary to Garrick's linear theory, there exists a pitching axis near the airfoil that maximizes propulsive efficiency. Next, we examine the effect of placing passive springs on the airfoil in the heave (transverse) direction using our Cyber-Physical Fluid Dynamics technique. This elastic heaving motion allows the airfoil to combine pitching and heaving modes while being actuated only in the pitching direction. Two sets of dynamics are considered: one case where the airfoil is weighted unevenly and pitched about its center of mass (so that the resulting heaving motion is independent of inertial forces), and another case where the airfoil's center of mass is fixed at its centroid. For pitching at an amplitude of $8^{\circ }$ and a reduced frequency $k$ of two, we find that elastic heave produces a maximum propulsive efficiency of 35%, compared to 25% without any heave motion. Further, while operating at the same efficiency as the static-pivot case, we find that passive heaving greatly increases the magnitude of the airfoil's thrust. The airfoil configurations with highest propulsive efficiency generally involve pitching near or ahead of the airfoil's leading edge.

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