Aerodynamic characteristics of a feathered dinosaur measured using physical models. Effects of form on static stability and control effectiveness

Abstract

We report the effects of posture and morphology on the static aerodynamic stability and control effectiveness of physical models based on the feathered dinosaur, [Formula: see text]Microraptor gui, from the Cretaceous of China. Postures had similar lift and drag coefficients and were broadly similar when simplified metrics of gliding were considered, but they exhibited different stability characteristics depending on the position of the legs and the presence of feathers on the legs and the tail. Both stability and the function of appendages in generating maneuvering forces and torques changed as the glide angle or angle of attack were changed. These are significant because they represent an aerial environment that may have shifted during the evolution of directed aerial descent and other aerial behaviors. Certain movements were particularly effective (symmetric movements of the wings and tail in pitch, asymmetric wing movements, some tail movements). Other appendages altered their function from creating yaws at high angle of attack to rolls at low angle of attack, or reversed their function entirely. While [Formula: see text]M. gui lived after [Formula: see text]Archaeopteryx and likely represents a side experiment with feathered morphology, the general patterns of stability and control effectiveness suggested from the manipulations of forelimb, hindlimb and tail morphology here may help understand the evolution of flight control aerodynamics in vertebrates. Though these results rest on a single specimen, as further fossils with different morphologies are tested, the findings here could be applied in a phylogenetic context to reveal biomechanical constraints on extinct flyers arising from the need to maneuver.

Figure 1. Microraptor gui from , a dromaeosaur from the Cretaceous Jiufotang Formation of Liaoning, China; physical models, and sign conventions.

A, Holotype specimen IVPP V13352, scale bar 5 cm. Notable features include semilunate carpal bones, a boomerang-shaped furcula, a shield-shaped sternum without a keel, uncinate processes on the ribs, unfused digits, an intermediate angle of the scapulocoracoid, and a long tail of roughly snout-vent length. In addition, there are impressions of feathers on the forelimbs, hindlimbs, and tail. B-J, Physical models of M. gui, scale model wingspan 20 cm, snout-vent-length 8 cm. Reconstruction postures, B-I, used for constructing physical models: B, sprawled, after ; C, tent, after , ; D, legs-down, after ; E, biplane, after . F-I additional manipulations: F, asymmetric leg posture with 9090 leg mismatch ( arabesque ); G, example asymmetric leg posture with 45 dihedral on one leg ( dégagé ), H, sprawled without leg or tail feathers; I, tent without leg or tail feathers. J, test setup; K, sign conventions, rotation angles, and definitions for model testing, after , , .

Figure 2. Nondimensional coefficients for all baseline postures.

Red is sprawled, blue is tent, green is biplane, purple is down. from –15 to 90 in 5 increments, with five or more replicates per treatment. A, Lift coefficient. B, Drag coefficient. C, Lift drag polars. D, Pitching moment coefficient. Stable angles of attack, which cross with negative slope, for tent (blue) and biplane (green) postures identified with yellow arrows.

Figure 3. Full scale forces and moments for M. gui at 12 .

Red is sprawled, blue is tent, green is biplane, purple is down. from –15 to 90 in 5 increments, with five or more replicates per treatment. Gray band indicates weight range of M. gui. A, Full scale lift at 12 , all models. B, Full scale drag at 12 , all models. C, Lift-drag polars. D, Full scale pitching moment at 12 versus angle of attack, all models. Stable angles of attack for tent (blue) and biplane (green) indicated.

Figure 4. Reynolds number sweeps for A, lift, B, drag, and C, pitch coefficients.

There are not large changes in aerodynamic coefficients over the ranges shown here. This is similar to what is seen in benchmarking tests with Draco lizard and Anna's Hummingbird (Calypte anna) models. The coefficients are roughly constant in the range of Archaeopteryx. Moment coefficients are constant over the range shown.

Figure 5. Presence or absence of leg and tail feathers can substantially alter longitudinal plane aerodynamics.

Sprawled and tent postures with and without feathers, all coefficients shown versus angle of attack, solid squares with leg and tail feathers, open squares without leg or tail feathers. A, Lift coefficient. Stall occurs at higher angle of attack when leg feathers are present. B, Drag coefficient. Leg feathers increase drag at high angle of attack, improving parachuting performance. C, Lift coefficient versus drag coefficient. D, Lift to drag ratio. Lift to drag ratio is improved slightly without the additional drag and less-efficient lift generation of hind wings. E, Pitching moment coefficient. Without leg feathers, stability is not achieved in either posture. F, Pitching stability coefficient.

Figure 6. Presence or absence of leg and tail feathers has effects on metrics, although the usefulness of is questionable (see Fig. S2).

Feathers present (black outline) or absent (grey outline) A, Maximum lift to drag ratio, by sprawled and tent postures with and without feathers. The maximum lift to drag ratio for tent without leg or tail feathers is significantly higher than for other postures (ANOVA, ), however, this improvement is never achieved because the tent posture is never stable without leg feathers. B, Minimum glide speed, by sprawled and tent postures with and without feathers. There are no differences in minimum glide speed between postures (ANOVA, ). C, Parachuting drag, by sprawled and tent postures with and without feathers. There are significant differences in parachuting drag between postures (ANOVA, ), however, the straight-down parachuting position is not stable.

Figure 7. At 0 angle of attack, there are clear differences in yaw stability between postures.

In particular, with legs down, the legs strongly act as weathervanes to stabilize the body in yaw (purple line, high slopes near 0 ). Color represents the base posture: red for sprawled, blue for tent, green for biplane, and purple for down.

Figure 8. There are also clear differences in yaw stability at different angles of attack.

A, At 0, some postures are more stable in yaw than others. B, At 60, postures that were stable at 0 may go unstable, such as tent posture. C, At 90, all postures are marginally stable due to symmetry (lines flat, yawing does not alter position relative to flow). Color represents the base posture: red for sprawled, blue for tent. Organisms may have navigated this transition from 90 to 0.

Figure 9. The differences in yaw stability at different angles of attack also depend on the presence or absence of leg feathers.

A, At 0, some feathered-leg postures are more stable in yaw than others. B, At 60, postures that were stable at 0 may go unstable, such as tent posture with leg feathers. C, At 90, all postures are marginally stable due to symmetry. Color represents the base posture: red for sprawled, blue for tent, green for biplane, and purple for down.

Figure 10. Tail control effectiveness for biplane posture for tail angles of -15 (down triangle), 0 (square), and +15 (up triangle).

At low angle of attack, tail up produces a nose up moment relative to zero tail angle, while tail down produces a nose down moment relative to zero tail angle. Tail movement is effective in trimming, by moving the point where the curve crosses . The small effect on lift suggests the tail is primarily effective because of moments generated by its long length.

Figure 11. Tail control effectiveness for down posture for tail angles of –15 (down triangle), 0 (square), and +15 (up triangle).

At low angle of attack, tail up produces a nose up moment relative to zero tail angle, while tail down produces a nose down moment relative to zero tail angle. Trimming to pitch stability with the tail is only possible with large 15 tail movement. At high angle of attack, the tail experiences reversal in which tail down produces nose up moments / tail up produces nose down moments.

Figure 12. Tail control effectiveness for sprawled posture for tail angles of –15 (down triangle), 0 (square), and +15 (up triangle).

With leg and tail feathers, A & C, and without, B & D. At low angle of attack, tail up produces a nose up moment relative to zero tail angle, while tail down produces a nose down moment relative to zero tail angle, C. Trimming with the tail is able to alter stability. Reversal is not seen at high angle of attack. Without leg feathers, D, the tail is ineffective at producing lift or pitching moment.

Figure 13. Tail control effectiveness for tent posture for tail angles of –30 (large down triangle), –15 (down triangle), 0 (square), +15 (up triangle), and +30 (large up triangle).

With, A & C, and without, B & D, leg or tail feathers. At low angle of attack, tail up produces a nose up moment relative to zero tail angle, while tail down produces a nose down moment relative to zero tail angle, C. Trimming with the tail is able to alter stability. Some reversal occurs at high angle of attack. Without leg feathers, the tail is ineffective at producing lift or pitching moment, B & D.

Figure 14. Leg control effectiveness for sprawled posture for leg angles of –15 (down triangle), 0 (square), and +15 (up triangle).

At low angle of attack, legs up produces a nose up moment relative to zero leg angle, while legs down produces a nose down moment relative to zero leg angle. Leg movement is slightly less effective at high angle of attack, and slightly less effective than tail movement.

Figure 15. Leg control effectiveness for tent posture for leg angles of –30 (large down triangle), –15 (down triangle), 0 (square), +15 (up triangle), and +30 (large up triangle).

With leg and tail feathers, A & C, and without, B & D. At low angle of attack, leg up produces a nose up moment relative to zero leg angle, while leg down produces a nose down moment relative to zero leg angle, C. Without leg feathers, the legs still have smaller effects, D. At high angles of attack, leg pitch effects become noisy and difficult to identify.

Figure 16. Symmetric wing sweep control effectiveness for tent posture for wing sweep angles of –45 (large down triangle), –22.5 (down triangle), 0 (square), +22.5 (up triangle) and +45 (large up triangle).

Wing sweep is very effective at generating pitching moments. Forward sweep generates nose up moments, while backwards sweep generates nose down moments. This is like steering a wind surfing rig and is similar to what is seen in Anna's Hummingbird ( Calypte anna ) dive models (Evangelista, in preparation). This mode of control exhibits reversal at negative angle of attack and thus may be difficult to use around 0 angle of attack.

Figure 17. Symmetric wing pronation/supination control effectiveness for tent posture for wing angles of –30 (large down triangle), –15 (down triangle), 0 (square), +15 (up triangle) and +30 (large up triangle).

Wing pronation/supination (wing angle of attack) is effective at changing the lift generated but exhibits reversal at high angle of attack where stall occurs.

Figure 18. Asymmetric wing sweep (e.g. left and right wings swept forward and backward) control effectiveness for tent posture for wing sweep angles of –45 (large down triangle), –22.5 (down triangle), 0 (square), +22.5 (up triangle) and +45 (large up triangle).

Forward sweep generates upward pitching moments, backward sweep generates downward pitching moments. Considerable roll moments are also generated at higher angles of attack. Non-zero roll moments for symmetrical postures (B, squares) is due to slight sting misalignment during test, illustrating the measurement noise of the test.

Figure 19. Asymmetric wing pronation (e.g. left and right wings pitched in opposite directions) control effectiveness for tent posture for wing pronation angles of –30 (large down triangle), –15 (down triangle), 0 (square), +15 (up triangle) and +30 (large up triangle).

At low angles of attack, asymmetric wing pronation generates large rolling moments. At high angles of attack, there is a shift in function and asymmetric wing pronation tends to generate yawing moments instead of rolling moments. Function at high angle of attack is similar to what is observed in human skydivers , . Organisms may have navigated this transition from high angle of attack to low.

Figure 20. Asymmetric wing tucking control effectiveness for tent posture; both wings out (solid square), no right wing (open square) and no wings (open diamond).

Tucking one wing produces large roll moments but at the expense of one quarter of the lift. Large yaw moments are not generated except at higher angles of attack where the leg and tail positions become more important. Rolling moments generated in the two-wing symmetric position illustrates the senstivity of symmetry, model positioning, and sting placement; in addition, yawing moments at extreme angle of attack further illustrate sensitivity to position which could be exploited as a control mechanism during high angle of attack flight.

Figure 21. Asymmetric leg dihedral (leg dégagé, see inset) effect on yaw.

Baseline down position (solid square) versus one leg at 45 dihedral (down arrow). Placing one leg at a dihedral is destabilizing in yaw and produces side force and rolling and yawing moments due to the asymmetry.

Figure 22. Asymmetric tail movement (lateral bending) effect on yaw, tent posture.

Baseline tent position (solid square), tail 10 left (open square), tail 20 left (open triangle), tail 30 left (open diamond). The tail is effective at creating yawing moments but at low angles of attack it is shadowed by the body and larger movements are needed (yellow versus red lines).

Figure 23. Asymmetric one wing down effect on yaw, tent posture.

Baseline tent position (solid square), left wing down (down triangle). Placing one wing down does not make large yawing moments. Some roll and side force is produced at low angles of attack, at the expense of one quarter to one half of the lift.