Normalized Lift: An Energy Interpretation of the Lift Coefficient Simplifies Comparisons of the Lifting Ability of Rotating and Flapping Surfaces
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{"title"=>"Normalized lift: An energy interpretation of the lift coefficient simplifies comparisons of the lifting ability of rotating and flapping surfaces", "type"=>"journal", "authors"=>[{"first_name"=>"Phillip", "last_name"=>"Burgers", "scopus_author_id"=>"7005168440"}, {"first_name"=>"David E.", "last_name"=>"Alexander", "scopus_author_id"=>"7402830653"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"doi"=>"10.1371/journal.pone.0036732", "sgr"=>"84861313028", "issn"=>"19326203", "pui"=>"364857594", "isbn"=>"1932-6203", "pmid"=>"22629326", "scopus"=>"2-s2.0-84861313028"}, "id"=>"70e2cecf-b761-3cbc-8d39-e677064388ee", "abstract"=>"For a century, researchers have used the standard lift coefficient C(L) to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv(2), 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, ½v(2). 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.", "link"=>"http://www.mendeley.com/research/normalized-lift-energy-interpretation-lift-coefficient-simplifies-comparisons-lifting-ability-rotati", "reader_count"=>13, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Researcher"=>5, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>3, "Student > Postgraduate"=>1, "Student > Bachelor"=>1, "Student > Master"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Researcher"=>5, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>3, "Student > Postgraduate"=>1, "Student > Bachelor"=>1, "Student > Master"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>6, "Agricultural and Biological Sciences"=>4, "Physics and Astronomy"=>1, "Energy"=>1, "Sports and Recreations"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>6}, "Energy"=>{"Energy"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Sports and Recreations"=>{"Sports and Recreations"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>4}}, "reader_count_by_country"=>{"Sweden"=>2, "United States"=>1}, "group_count"=>1}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/634557"], "description"=>"<p>Normalized lift <i>L<sub>N</sub></i> equations for different lift-generating systems.</p>", "links"=>[], "tags"=>["equations", "lift-generating"], "article_id"=>305050, "categories"=>["Physiology", "Physics"], "users"=>["Phillip Burgers", "David E. Alexander"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0036732.t001", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Normalized_lift_L_N_equations_for_different_lift_generating_systems_/305050", "title"=>"Normalized lift <i>L<sub>N</sub></i> equations for different lift-generating systems.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-05-21 01:24:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/634518"], "description"=>"*<p>Note that <i>c<sub>ave</sub></i> and <i>φ<sub>ps</sub></i> values are only needed when pronation and supination are included in the normalized lift calculation.</p><p>Sources:</p>1<p><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036732#pone.0036732-Norberg1\" target=\"_blank\">[8]</a>;</p>2<p><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036732#pone.0036732-Wolf1\" target=\"_blank\">[14]</a>;</p>3<p><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036732#pone.0036732-Ennos1\" target=\"_blank\">[7]</a>.</p>", "links"=>[], "tags"=>["reported", "calculated", "normalized", "assumed", "kg"], "article_id"=>305014, "categories"=>["Physiology", "Physics"], "users"=>["Phillip Burgers", "David E. Alexander"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0036732.t002", "stats"=>{"downloads"=>1, "page_views"=>39, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Morphometric_data_reported_standard_lift_coefficients_and_calculated_normalized_lift_values_air_density_is_assumed_to_be_1_2_kg_m_8722_3_/305014", "title"=>"Morphometric data, reported standard lift coefficients, and calculated normalized lift values (air density is assumed to be 1.2 kg m<sup>−3</sup>).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-05-21 01:23:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/634471"], "description"=>"<p>Lift to drag ratio, <i>L/D</i>, standard lift coefficient, <i>C<sub>L</sub></i>, and normalized lift, <i>L<sub>N</sub></i>, (all dimensionless ratios), plotted against spin parameter (<i>u<sub>T</sub>/v<sub>∞</sub></i>) for a rotating cylinder in Magnus effect. Data from Reid (1924).</p>", "links"=>[], "tags"=>["rotating"], "article_id"=>304973, "categories"=>["Physiology", "Physics"], "users"=>["Phillip Burgers", "David E. Alexander"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0036732.g001", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Coefficients_for_a_rotating_cylinder_/304973", "title"=>"Coefficients for a rotating cylinder.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-21 01:22:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/328377", "https://ndownloader.figshare.com/files/328420"], "description"=>"<div><p>For a century, researchers have used the standard lift coefficient <em>C<sub>L</sub></em> to evaluate the lift, <em>L</em>, generated by fixed wings over an area <em>S</em> against dynamic pressure, <em>½ρv</em><sup>2</sup>, where <em>v</em> 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.</p> <p>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 (<em>L/ρ·S</em>), compared against the total kinetic energy required for generating said lift, <em>½v<sup>2</sup></em>. 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.</p> <p>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.</p> </div>", "links"=>[], "tags"=>["normalized", "coefficient", "simplifies", "comparisons", "lifting", "rotating", "flapping", "surfaces"], "article_id"=>124822, "categories"=>["Physiology", "Physics"], "users"=>["Phillip Burgers", "David E. Alexander"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0036732.s001", "https://dx.doi.org/10.1371/journal.pone.0036732.s002"], "stats"=>{"downloads"=>11, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Normalized_Lift_An_Energy_Interpretation_of_the_Lift_Coefficient_Simplifies_Comparisons_of_the_Lifting_Ability_of_Rotating_and_Flapping_Surfaces/124822", "title"=>"Normalized Lift: An Energy Interpretation of the Lift Coefficient Simplifies Comparisons of the Lifting Ability of Rotating and Flapping Surfaces", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-05-21 01:20:22"}

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Relative Metric

{"start_date"=>"2012-01-01T00:00:00Z", "end_date"=>"2012-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Organisms", "average_usage"=>[331, 557, 677, 777, 868, 960, 1050, 1136, 1223, 1307, 1390, 1466, 1536, 1603, 1673, 1741, 1814, 1889, 1954, 2028, 2096, 2164, 2233, 2305, 2362]}, {"subject_area"=>"/Biology and life sciences/Physiology", "average_usage"=>[307, 536, 653, 753, 839, 926, 1017, 1103, 1189, 1268, 1348, 1425, 1492, 1557, 1620, 1686, 1759, 1825, 1891, 1950, 2014, 2079, 2141, 2200, 2255]}, {"subject_area"=>"/Biology and life sciences/Veterinary science", "average_usage"=>[368, 635, 753, 861, 975, 1103, 1205, 1302, 1411, 1512, 1630, 1714, 1767, 1840, 1918, 1992, 2095, 2196, 2254, 2308, 2385, 2438, 2520, 2604, 2682]}, {"subject_area"=>"/Engineering and technology", "average_usage"=>[308, 500, 607, 700, 782, 876, 957, 1039, 1128, 1214, 1290, 1365, 1431, 1496, 1560, 1634, 1695, 1772, 1839, 1908, 1972, 2043, 2106, 2179, 2246]}, {"subject_area"=>"/Engineering and technology/Mechanical engineering", "average_usage"=>[277, 417, 499, 563, 614, 691, 756, 808, 871, 953, 1017, 1101, 1150, 1190, 1237, 1290, 1345, 1406, 1455, 1546, 1614, 1656, 1705, 1736, 1770]}]}
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