Linearizing resistive forces and adding other model terms

We added to these basic equations kinematic variables which we had a priori reason to expect might contribute to moth directional movement, and then applied a stepwise variable elimination approach. Here, , which is roughly equivalent to sin (θ_i), represents drag on the wing ipsilateral to the directional or rotational movement. We attempted to fit this kinematic because the wing ipsilateral to the movement direction is exposed to both lateral velocity and roll velocity. We report the attempted fit of this measurement for completeness since we used all attempted kinematics when calculating P-values. Since we are interested in how departures from typical flapping leads to the creation of movement, we used the mean-centered versions of and . In Eqn 6, subtracting the overall mean isolates variance and thus allows us to multiply by sign(β) to estimate coefficients. In Eqns 7-8, mean-centering and allows us to assume a zero intercept; a significant intercept result would indicate moth-specific variation or that our model fails to represent the complete moth system maneuver dynamics.

In the most general sense, high Reynolds number air drag is proportional to velocity squared. However, the velocities moths encountered in our experiments cover a small range, over which we might expect to reasonably linearize an exponential trend. Furthermore, computational analysis of the flight of M. sexta suggests that, on the time scale of half wing-strokes, passive resistance to movement during horizontal and vertical movement is roughly linearly proportional to velocity rather than velocity squared for both horizontal and vertical movement terms, (Cheng and Deng, 2011; Kim and Han, 2014). Further velocity damping effects have also been proposed (Faruque and Humbert, 2010). Linearizing the resistive forces and adding other model terms resulted in the following equations, (see Expected coefficient values for predictions):