Diving-flight aerodynamics of a peregrine falcon (Falco peregrinus)

Abstract

This study investigates the aerodynamics of the falcon Falco peregrinus while diving. During a dive peregrines can reach velocities of more than 320 km h⁻¹. Unfortunately, in freely roaming falcons, these high velocities prohibit a precise determination of flight parameters such as velocity and acceleration as well as body shape and wing contour. Therefore, individual F. peregrinus were trained to dive in front of a vertical dam with a height of 60 m. The presence of a well-defined background allowed us to reconstruct the flight path and the body shape of the falcon during certain flight phases. Flight trajectories were obtained with a stereo high-speed camera system. In addition, body images of the falcon were taken from two perspectives with a high-resolution digital camera. The dam allowed us to match the high-resolution images obtained from the digital camera with the corresponding images taken with the high-speed cameras. Using these data we built a life-size model of F. peregrinus and used it to measure the drag and lift forces in a wind-tunnel. We compared these forces acting on the model with the data obtained from the 3-D flight path trajectory of the diving F. peregrinus. Visualizations of the flow in the wind-tunnel uncovered details of the flow structure around the falcon's body, which suggests local regions with separation of flow. High-resolution pictures of the diving peregrine indicate that feathers pop-up in the equivalent regions, where flow separation in the model falcon occurred.

Figure 1. Experimental set-up in front of the dam wall (Olef-Talsperre, Hellenthal, Germany).

The two cameras of the stereo system were positioned opposite, separated by a river leaving the dam wall. The features, displayed on the wall enabled us to calibrate the stereo camera system and to exactly determine the position of the diving falcon in the images of both cameras.

Figure 2. Top-view of the experimental set-up with all measurement components.

Figure 3. Reprojection error after calibration.

The mean values are 0.23 pixel in x- and 0.07 pixel in y-direction.

Figure 4. Transformation from a real falcon (A) to a life-size model (B).

Pictures from (A) were taken during the diving flights of a peregrine in front on the dam wall. The open wing-shape configuration of the flight was transformed (B).

Figure 5. One-to-one falcon model and the measuring device inside the wind-tunnel (A). Functionality scheme of the force-balances (B).

Figure 6. Drag coefficient for flow across a sphere as a function of the Reynolds number.

A: data from Krause . B: measured data by the force balances with typical values documented in the literature as well as the abrupt decrease of the drag at a Reynolds number of about 3.5*10⁵.

Figure 7. Detail studies for the specific wing shapes.

Figure 8. Three-dimensional orientation of the camera set-up based on the spatial calibration.

The reconstructed 3-D flight path of the falcon is color-coded with the flight velocity magnitude (red-colored: higher velocities). Maximum velocity during the dive was 22.5 m s⁻¹.

Figure 9. Side-view (left) and front-view (right) of the dam wall and the color-coded trajectory.

The six sections of the flight path are acceleration/diving phase (1), transient phase with roughly constant speed (2), deceleration and flight path corrections phase (3), pull out phase (4), landing phase with constant speed (5) and deceleration with touchdown (6).

Figure 10. Velocity magnitude (A) and acceleration (B) of the falcon during the time pathway flight.

Spline interpolation of the data with the aid of a moving 3^rd-order-polynomial approximation.

Figure 11. Variation of flight path angle θ in the major tracking phase.

The bird starts from almost vertical flight (θ = 90° relative to the horizontal) and still had a flight path angle of θ = 70° when it entered the tracking area (t = 0). The light path angle decreased then continuously until the bird pulled out (θ = 0°) at 2.3 s. The flight path angle is about 50.75° when the bird reached the maximum velocity.

Figure 12. Forces acting at the falcon during diving at maximum speed and zero acceleration.

For the given flight path angle θ only one angle of attack α leads to the fulfilled condition of equilibrium.

Figure 13. Polar diagram of the falcon model for a velocity of 22.5⁻¹.

The angles of attack α varied from −15° to +37°. The increase of the pole line (black dashed line) of the open wing shape is m = 1.93 for the best gliding angle of α_g = 21°. The increase of the linear function (red dashed line) for the equilibrium condition is m = 1/tan(θ) = 1.22. Hence the intersection of this linear function with the polar curve leads to an angle of attack α_e = 5° in the free flight situation.

Figure 14. Drag coefficient vs. Reynolds number of the falcon model for different angles of attack α.

Measurements were done for different Reynolds numbers [Re = 260 000 (v = 10 m s⁻¹), Re = 585 000 (v = 22.5 m s⁻¹), Re = 780 000 (v = 30 m s⁻¹) and Re = 1 040 000 (v = 40 m s⁻¹)].

Figure 15. Flow visualization on the surface of the falcon model via oil-based painting.

A: top-view, B: frontal side-view. (Re = 5.8 10⁵, angle of attack α = 5°, flow direction is from left to right).

Figure 16. Flow visualization on the surface of the falcon model via oil-based painting (A) and the living creature at the identical flight position (B).

The area of the red circle shows a homogenous white colored oil-painting. This indicates a local separation of flow. The falcon on the right-hand side shows small feathers which are popped-up from the falcon body in this region. It is assumed that this specific arrangement of the feathers prevents local flow separation on the falcon body in nature.

Figure 17. Flow visualization in four cross-sections of the falcon model via particle image velocimetry (PIV).

Layer one goes through the plane of symmetry whereas layers two to four have an offset in each case of 14-painted top-view of the model shows that only layer two crosses the region where a higher intensity of oil indicates area where local flow separation is seen. Exactly in this region the PIV results show a dead water region in comparison to the other layers.