Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster...

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Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster projects •Recap drag and the Reynolds number •Drag and its coefficient •How size, shape, and the Reynolds number determine drag •Streamlined bodies and swimming energetics •When does drag matter?

Transcript of Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster...

Page 1: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Zoology 427 BiomechanicsLecture 18. Shape and drag

•A comment about poster projects•Recap drag and the Reynolds number•Drag and its coefficient•How size, shape, and the Reynolds number determine drag

•Streamlined bodies and swimming energetics•When does drag matter?

Page 2: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

(P2 - P1) /ρ = (u12- u2

2 )/2PE + KE + W + Ediss = const

new stagnation point where the flow separates

Wake

Because of viscosity, velocity cannot increase as much as in the inviscid case.

Pressure stress: P ~ ρ u2

Shear stress: τ ~ µ du/drρ u L

µRe =

Page 3: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Drag force arises from pressure and frictional stresses D ~ ρ u2/2

D = Cd ρ S u2/2drag coefficient projected surface area

sizeshapeReynolds number

!" =$

12'()*

!

Page 4: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Shape and Drag

1.25 1.14 0.5 0.3 0.045

!" =$

12'()*

!

Flow

Page 5: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Log Reynolds number

Cd

-1 0 1 2 3 4 5 6 7 8

100

10

1

0.1

!" =$

12'()*

!

streamlined body: same surface area

roughness

!" =24&' +

61 + &' + 0.4!

von Karmanvortex street

Page 6: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Streamlining – how much?

LD

Fineness ratio = L/D

manage your wake and the adverse pressure gradient

Page 7: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

LD

Fineness ratio = L/D

Challenge: you are given a fixed volume of fish and must arrange it to minimize the total drag. The volume can be distributed with any fineness ratio. Generate a hypothetical plot for the drag as a function of fineness ratio.

Streamlining – how much? manage your wake and the adverse pressure gradient

Page 8: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Streamlining – how much?D

rag

Fineness ratio = L/D

Page 9: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

“You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes”. JBS Haldane 1926. On Being the Right Size.

D = 0.5 Cd ρ S u2

m g

m g = 0.5 Cd ρ S u2

! = #$% = $#$ 43 ()*! ! = #$%&!

Page 10: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

D = 0.5 Cd ρ S u2

m g

m g = 0.5 Cd ρ S u2

! = #$% = $#$ 43 ()*! ! = #$%&!

u

r

Assume ρ, g,Cd : const.

Page 11: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Drag is a propulsive force

Page 12: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

Drag is a propulsive forceDrag on oar generates thrust

Thrust = DragThrust = Drag

Drag * Velocity = Power output

Thru

st

0 Piangle

Page 13: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

When does drag matter?

Energy What is the average power per strideif we consider drag?

(1 − $)& '(&)

8+ +'+-

2) + 12/012+-!

Page 14: Zoology 427 Biomechanics Lecture 18. Shape and drag •A comment about poster …courses.washington.edu/biomechs/lectures/lecture18.pdf · 2016-11-06 · Zoology 427 Biomechanics

D =

0.5

Cd ρ

S u

2

m g!

=#$%

=$#$4 3(

)*!

!=#$%

& !

u

r

Assu

me ρ,

g,C

d : c

onst

.

DragFo

r a fi

xed

volu

me