Table 4.

Summary of studies assessing the relationship between wingbeat frequency, amplitude and mechanical power output.

species	method	flight mode	speed (m s−1)	remarks	source
pigeon Columba livia	field data—GPS and accelerometer measurements	level, ascending and descending flight, all while circling	10–18	as speed increased	Usherwood et al. [6]
				WBF—varied approx. U shaped
				WBA—increased
				at constant speed, as power increased
				WBF—increased
				WBA—decreased
				ascending flight
				WBF—increased
				WBA—increased
				accelerating flight
				WBF—increased
				WBA—increased
pigeon Columba livia	platform—muscle force measurements and kinematic analysis with high-speed cameras	ascending, level and descending	1.4–3.9	in different flight modes	Tobalske & Biewener [30]
				WBF—did not vary significantly
				WBA—decreased during take-off and prior to landing
common starling Sturnus vulgaris	wind tunnel—respirometry masks and kinematics analysis with high-speed cameras	level flight	6–14	as speed increased	Ward et al. [27]
				WBF—increased (less significant)
				WBA—increased (less significant)
				power—increased
Eurasian tree sparrow Passer montanus	experiments in flight chamber—kinematics analysis with high-speed cameras	vertical flight	—	as maximum load lifted	Wang et al. [32]
				WBF—no significant variation
				WBF—no significant variation
barn swallow Hirundo rustica	wind tunnel—energetic costs measured by DLW, and kinematics analysis is by video recordings	level flight	8–11.5	as speed increased	Schmidt-Wellenburg et al. [23]
				WBF—varied as U shaped
				as mass increased
				WBF—increased
				power—increased
blue tit Cyanistes caeruleus	flight inside a custom-built box—kinematics analysis with high-speed cameras	take-off	3.4	as wing loading increased	McFarlane et al. [58]
				WBF—decreased
				WBA—did not vary
				power—decreased
				AR—increased
thrush nightingale Luscinia luscinia	wind tunnel—PIV and kinematics analysis with high-speed cameras	level flight	5–10	as speed increased	Rosén et al. [25]
				WBF—no significant variation
				WBA—no significant variation
thrush nightingale Luscinia luscinia	wind tunnel—wingbeat frequency measured using a shutter stroboscope and video recording	level flight	5–16	as mass increased	Pennycuick et al. [22]
				WBF—increased
				as speed increased
				WBF—varied in U shape (less significantly)
zebra finch Taeniopygia guttata	wind tunnel—kinematics analysis with high-speed cameras	intermittent flap-bounding flight	0–14	as speed increased	Tobalske et al. [59]
				WBF—increased (less significant)
				WBA—decreased (significantly)
zebra finch Taeniopygia guttata	surgical procedures to measure flight muscle activity	?	—	as power increased	Bahlman et al. [60]
				WBF—no significant effect
				WBA—increased effectively
zebra finch Taeniopygia guttata	wind tunnel—muscle in vivo pectoralis fascicle strain measurements, and kinematics by high-speed video recordings	level flight	0–14	as speed increased	Ellerby & Askew [20]
				WBF—varied approx. U shaped
				WBA—increased only at hovering
budgerigar Melopsittacus undulates	wind tunnel—muscle in vivo pectoralis fascicle strain measurements, and kinematics by high-speed video recordings	level flight	4–16	as speed increased	Ellerby & Askew [20]
				WBF—varied approx. U shaped
				WBA—did not vary significantly
cockatiel Nymphicus hollandicus	wind tunnel—in vivo pectoralis muscle length change measurements	level flight	0–16	as speed increased	Morris & Askew [61]
				power—increased (approx. U shaped)
				WBF—reduced (highest at the lower range)
cockatiel Nymphicus hollandicus	wind tunnel—in vivo surgical procedures and kinematics analysis with high-speed cameras	level flight	0–14	as speed increased	Hedrick et al. [21]; Tobalske et al. [19]
				WBF—reduced at lower speed and increased at higher speed (approx. U shaped)
				power—varied (approx. U shaped)
Eurasian teal Anas crecca	wind tunnel—wingbeat frequency measured using a shutter stroboscope and video recording	level flight	5–16	as mass increased	Pennycuick et al. [22]
				WBF—increased
				as speed increased
				WBF—varied in U shape (less significantly)
black-legged kittiwake Rissa tridactyla	wild study—kinematics and airspeed data of commuting flights measured using GPS and accelerometer devices	flap–glide flight (predominantly flapping)	2–16	as speed increased	Collins et al. [62]
				WBF—no significant relationship
				WBA—increased significantly (as proxy by body moving amplitude)
Harris's hawk Parabuteo unicinctus	outdoor flight—accelerometery data and kinematic analysis using video recordings	climbing flight	—	as climb power increased	Van Walsum et al. [13]
				WBF—increased linearly with lesser variation
				WBA—increased linearly with higher variation (as proxy by body moving amplitude)
common swift Apus apus	wind tunnel—PIV and kinematics analysis with high-speed cameras	level flight	8–9.2	as speed increased	Henningsson et al. [63]
				WBF—decreased
				WBA—increased
ruby-throated hummingbird Archilochus colubris	flight experiments in an airtight cube—varying air density treated with heliox	hovering	—	as power increased	Chai & Dudley [64]
				WBF—increased (less significant)
				WBA—increased (significantly)
				as air density decreased
				power—increased
ruby-throated hummingbird Archilochus colubris	flight experiments in an airtight cube—varying air density treated with helium	hovering	—	as power increased	Chai & Dudley [65]
				WBF—did not vary
				WBA—increased (significantly)
				as air density decreased
				power—increased
ruby-throated hummingbird Archilochus colubris	cubic testing arena—surgical procedures to measure flight muscle activity and kinematics analysis with high-speed cameras	hovering	—	as load lifted increased	Mahalingam & Welch [66]
				WBF—did not vary
				WBA—increased (significantly)
				as air density decreased
				WBF—did not vary
				WBA—increased (significantly)
rufous hummingbird Selasphorus rufus	wind tunnel—kinematics analysis with high-speed cameras	hovering and level flight	0–12	as speed increased	Tobalske et al. [67]
				WBF—did not vary
				WBA—increased (approx. U shaped)