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J R Soc Interface. 2015 Apr 6;12(105). pii: 20150051. doi: 10.1098/rsif.2015.0051.

Power reduction and the radial limit of stall delay in revolving wings of different aspect ratio.

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Department of Mechanical Engineering, Stanford University, Stanford, CA, USA Experimental Zoology Group, Wageningen University, Wageningen, The Netherlands.
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands.
Department of Zoology, University of British Columbia, Vancouver, BC, Canada.
Department of Mechanical Engineering, Stanford University, Stanford, CA, USA


Airplanes and helicopters use high aspect ratio wings to reduce the power required to fly, but must operate at low angle of attack to prevent flow separation and stall. Animals capable of slow sustained flight, such as hummingbirds, have low aspect ratio wings and flap their wings at high angle of attack without stalling. Instead, they generate an attached vortex along the leading edge of the wing that elevates lift. Previous studies have demonstrated that this vortex and high lift can be reproduced by revolving the animal wing at the same angle of attack. How do flapping and revolving animal wings delay stall and reduce power? It has been hypothesized that stall delay derives from having a short radial distance between the shoulder joint and wing tip, measured in chord lengths. This non-dimensional measure of wing length represents the relative magnitude of inertial forces versus rotational accelerations operating in the boundary layer of revolving and flapping wings. Here we show for a suite of aspect ratios, which represent both animal and aircraft wings, that the attachment of the leading edge vortex on a revolving wing is determined by wing aspect ratio, defined with respect to the centre of revolution. At high angle of attack, the vortex remains attached when the local radius is shorter than four chord lengths and separates outboard on higher aspect ratio wings. This radial stall limit explains why revolving high aspect ratio wings (of helicopters) require less power compared with low aspect ratio wings (of hummingbirds) at low angle of attack and vice versa at high angle of attack.


aspect ratio; hover; hummingbird; leading edge vortex; revolving wing; stall delay

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