On the Validity of the Normal Force Model for Steadily Revolving Wings: An Experimental Investigation

Abstract

Aerodynamic characteristics of revolving wing models were investigated to assess the validity of the normal force model. Aerodynamic force and torque measurements were conducted for six wing planforms (with aspect ratios of 2 and 3, and area centroid locations at 40%, 50%, and 60% of the wing length) at three different Reynolds numbers (0.5 × 104, 1 × 104, and 1.5 × 104) and three thickness-to-chord ratios (3%, 4%, and 5%). Both early and steady phase measurements were extracted for a range of angles of attack relevant to insect flight. It was shown that the so-called “normal force” model conveniently captures the variation of the lift and drag coefficients along the first quadrant of angles of attack for all cases tested. A least squares best fit model for the obtained experimental measurements was used to estimate the key parameters of the normal force model, namely the lift curve slope, the zero-lift drag coefficient, and the peak drag coefficient. It was shown that the knowledge of only the lift curve slope and the zero-lift drag coefficient is sufficient to fully describe the model, and that clear trends of these two parameters exist. Notably, both parameters decreased with the increase in area centroid location. For instance, for steady measurements and on average, the lift curve slope for a wing with an area centroid location at 40% span was 15.6% higher compared to an area centroid location at 60% span. However, the increase in the zero-lift drag coefficient for wings with a lower area centroid location had a detrimental effect on aerodynamic efficiency assessed via glide ratio. Wings with a lower area centroid location consistently led to a lower glide ratio regardless of the change in aspect ratio, thickness-to-chord ratio, or Reynolds number. Increasing the aspect ratio decreased the zero-lift drag coefficient but generally had a slighter increasing effect on the lift curve slope. Increasing the Reynolds number within the range experimented decreased both the lift curve slope and the zero-lift drag coefficient. Finally, the effect of the thickness-to-chord ratio was mainly pronounced in its effect on the zero-lift drag coefficient.