Smoke visualization of free-flying bumblebees indicates independent leading-edge vortices on each wing pair

Span efficiency in hawkmoths

“…Trajectories were filtered beneath wingbeat frequency, and the average flight speed was calculated using numerical differencing of the positional data (cf. [15]). The mean of the modal flight speeds, of three to five sequences for each individual within the species, was taken as the preferred flight speed of that species and used for setting the wind tunnel speeds during the tethered Wind tunnel experiments for each individual were performed within a day and typically over the course of 4-5 h. The wing condition of the moths was monitored continuously throughout the experimental session, and the moths were fed periodically with a honey solution (honey and water, 1 : 10).…”

“…In most cases, the wakes of animals incorporate several distinctly different vortex elements, such as wingtip and wing root vortices (e.g. craneflies [18]; bees [15]; bats [19]; flycatchers [11]; swifts [20] and blackcaps [21]). Using PIV, it is possible to capture these vortex elements as they are shed behind the flying insect.…”

“…Several studies of animal wakes have shown the presence of wing root vortices and they seem to form either as an effect of the body disrupting the downwash profile or by petiolation of the wing planform. Two striking examples are the bumble-bee [15] and the cranefly [17]: in both cases, the left and right wings generate almost completely independent wakes (cf. [25]).…”

“…Regardless of the mechanistic reason for this mismatch, it is a costly way to fly because, in effect, it means that by the time the downwash distribution has reached its most efficient configuration, the majority of the lift has already been generated. On the other hand, it may be that, similar to bumble-bees, it is beneficial for moths to retain aerodynamic independence between the two wing pairs for control authority and to facilitate manoeuvring [15].…”

Optimum hovering wing planform

“…Thus, we find it necessary to further develop the approach by setting the circulation strength along the wing to an elliptic distribution which from lifting line theory is known to produce a constant downwash velocity distribution [15,16]. Since lift and hence bound circulation falls to zero at the inboard edge of the wing and there is no carryover of lift to the opposite wing [9,17,18] [19]. This optimum chord distribution is shown in Fig.…”