Biology 427 BiomechanicsLecture 20 Gliding flight: a soar topic.

•Recap basics of lift and circulation

•The lift coefficient (CL) and aspect ratio

•Drag coefficients for wings•Drag and lift together (polar plots)•Gliding flight – gravity, drag and lift•Soaring flight – gravity, drag, lift, and natural currents

Lift and Circulation:Subtract the mean velocity from all of these vectorsL = CL ρ S U2/2

With the mean subtracted, there is an effective circulation ( Γ )about the wing. Greater Γ implies a greater velocity difference

Lift and Circulation:

Circulation can be lost from the wing as a tip vortex

Message: lift can be measured by the amount of circulation held by a wing

Higher aspect ratio wings loose proportionately less

Formation flight: recovers some lost

Lift and Circulation:

For real wings in real fluids, we cannot ignore viscosity and the finite span of the wings.

CL = 2 L / ρ S U2

planform area

α

CL

high Re

low Re

shape, camber, texture, Reynolds number

1.4

1.2

1.0

0.8

0.6

0.4

0.2

00 0.2 0.4 0.6 0.8 1.0

Polar plots of wings

CL

CD

NACA airfoil

19.5

22

0

locust25

30

0

fly

0

25 30 50

Where, for locust wings, is the ratio of lift to drag greatest?A, B, C?

A

BC

L = CL ρ S U2/2 D = CD ρ S U2/2

perpendicularparallel

Gliding: “falling with style”

Gliding: “falling with style”

Gliding: “falling with style”

Gliding: “falling with style”

Gliding: “falling with style”

mg mgU1 U2

θ2θ1

Gliding: “falling with style”

1: Draw the forces (lift and drag)2: How does the glide angle depend on the ratio of lift to drag?

Weight = mg

Drag

Lift

θ

U

At equilibriumL = m g sin(θ) andD = m g cos (θ)D/L = cos (θ)/ sin(θ)

θ = tan-1(D/L) = tan-1(CD/CL) = cot-1(CL/CD)

GLIDING: how does weight affect trajectory?

use external currents to compensate for descending velocity

slope soaring

wave soaring

Soaring: gliding without much falling

use external currents to compensate for descending velocity thermal soaring

dynamic soaring

Soaring: gliding without much falling

Flapping flight: powering lift and thrust

mg mgU1 U2

θ2θ1

1: Draw the forces (lift and drag)2: How does the glide angle depend on the ratio of lift to drag?

How does weight affect trajectory?