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The aerodynamics of revolving wings II. Propeller force coefficients from mayfly to quail

James R. Usherwood^* and Charles P. Ellington

Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
^* Present address: Concord Field Station, MCZ, Harvard University, Old Causeway Road, Bedford, MA 01730, USA

View larger version (20K): [in a new window]   Fig. 1. Model hawkmoth planforms with a range of aspect ratios (AR) (A) and bumblebee planform (B). Wing lengths R: model hawkmoth R=0.5 m; real bumblebee R=12.86 mm; model bumblebee R=0.5 m.

View larger version (22K): [in a new window]   Fig. 2. The mini-spinner set up for small vertical force (A) and torque (B) measurements.

View larger version (31K): [in a new window]   Fig. 3. Model and real wing planforms for mayfly (forewing) (A) and quail (B). Wing lengths R: real mayfly R=13 mm; model mayfly R=50 mm; model and real quail R=100.1 mm.

View larger version (24K): [in a new window]   Fig. 4. Horizontal (Ch) (A,C) and vertical (Cv) (B,D) `propeller' force coefficients over a range of angles of incidence ' under `early' (A,B) and `steady' (C,D) conditions for model hawkmoth wings with a range of aspect ratios (AR). Grey lines show `early' and `steady' coefficients for `pooled' standard hawkmoth from Usherwood and Ellington (2002).

View larger version (10K): [in a new window]   Fig. 5. The relationship between maximum horizontal force coefficient (Ch) (at an angle of attack of 90°) and aspect ratio (AR) for revolving model hawkmoth wings under `early' and `steady' conditions. Error bars show ± 1 S.E.M. (N=4).

View larger version (13K): [in a new window]   Fig. 6. The rate of change of vertical force coefficient (Cv) with angle of incidence ('), dCv/d' for `early' and `steady' conditions from '=-20 to +20° for model hawkmoth wings with a range of aspect ratios (AR). Bars show 95 % confidence intervals (N=10). Differences both between high and low aspect ratios for either condition and between `early' and `steady' conditions for each aspect ratio are significant (P<0.01). The slopes of the regressions of dCv/d' against AR for `early' and `steady' conditions are not significantly different and average 0.130.

View larger version (23K): [in a new window]   Fig. 7. Horizontal (Ch) (A) and vertical (Cv) (B) force coefficients under `early' and `steady' conditions for model bumblebee wings over a range of angles of incidence '. Grey lines show `early' (higher) and `steady' (lower) coefficients for standard `pooled' hawkmoth.

View larger version (27K): [in a new window]   Fig. 8. Steady horizontal (Ch,steady) (A) and vertical (Cv,steady) (B) propeller coefficients for a range of wing types. Error bars show ±1 S.E.M. (N=4-10). ', angle of incidence.

View larger version (25K): [in a new window]   Fig. 9. `Early' horizontal (Ch,early) (A) and vertical (Cv,early) (B) propeller coefficients for model hawkmoth wings over a range of aspect ratios (AR). The model relationship given by Dickinson et al. (1999) for Drosophila is overlaid. ', angle of incidence.

View larger version (27K): [in a new window]   Fig. 10. Conversion of `steady' propeller coefficients into conventional profile drag (CD,pro) and lift (CL) coefficients using the models described in Usherwood and Ellington (2002) for a range of aspect ratios (AR). Ch, horizontal propeller coefficient; Cv, vertical propeller coefficient; , geometric angle of attack.

View larger version (16K): [in a new window]   Fig. 11. Polar diagrams for model hawkmoth wings with a range of aspect ratios (AR) under `early' (A) and `steady' (B) conditions. Points give the measured values; lines are derived from the normal force relationship. Ch, horizontal force coefficient; Cv, vertical force coefficient.