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dc.contributor.authorBurgers, Phillip
dc.contributor.authorAlexander, David E.
dc.date.accessioned2014-03-17T21:28:32Z
dc.date.available2014-03-17T21:28:32Z
dc.date.issued2012-05-21
dc.identifier.citationBurgers P, Alexander DE (2012) Normalized Lift: An Energy Interpretation of the Lift Coefficient Simplifies Comparisons of the Lifting Ability of Rotating and Flapping Surfaces. PLoS ONE 7(5): e36732. http:/dx.doi.org/10.1371/journal.pone.0036732
dc.identifier.urihttp://hdl.handle.net/1808/13185
dc.description.abstractFor a century, researchers have used the standard lift coefficient CL to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.

This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ½v2. This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.

The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.
dc.publisherPublic Library of Science
dc.rights© 2012 Burgers, Alexander. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectBat Flight
dc.subjectClassical mechanics
dc.subjectDrag
dc.subjectFlow feild
dc.subjectMoment of inertia
dc.subjectRotors
dc.subjectVelocity
dc.subjectWings
dc.titleNormalized Lift: An Energy Interpretation of the Lift Coefficient Simplifies Comparisons of the Lifting Ability of Rotating and Flapping Surfaces
dc.typeArticle
kusw.kuauthorAlexander, David E.
kusw.kudepartmentDepartment of Ecology and Evolutionary Biology
kusw.oastatusfullparticipation
dc.identifier.doi10.1371/journal.pone.0036732
kusw.oaversionScholarly/refereed, publisher version
kusw.oapolicyThis item meets KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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© 2012 Burgers, Alexander. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Except where otherwise noted, this item's license is described as: © 2012 Burgers, Alexander. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.