Biology 427 Biomechanics Lecture 20 Gliding flight: a soar topic. •Recap basics of lift and circulation • The lift coefficient (C L ) 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
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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?
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