“…From Eqns 9 and 10, we see that to prescribe the flapping motion, the stroke amplitude Φ, the wingbeat frequency n, the time duration of wing rotation Δt r , the angles of attack in the downstroke and upstroke translations α d and α u , and the mean positional angle φ must be given. Morphological and wing motion parameters for the dronefly are taken from the data of Liu and Sun (Liu and Sun, 2008) and that for the hawkmoth from the data of Willmott and Ellington (Willmott and Ellington, 1997a;Willmott and Ellington, 1997b). It should be noted that moments and products of inertia of the wing are not given in these references and they are estimated using the data of Liu and Sun, Willmott and Ellington, and Ennos (Liu and Sun, 2008;Willmott and Ellington, 1997a;Willmott and Ellington, 1997b), according to the density distribution of a dronefly wing measured by Ennos (Ennos, 1989b).…”