Magnus gliderNikita Grushetzky

Vitalii MatiuninStepan Zakharov

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The problem

Glue the bottoms of two light cups together to make a glider. Wind an elastic band around the centre and hold the free end that remains. While holding the glider, stretch the free end of the elastic band and then release the glider. Investigate its motion.

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FirstFirstobservationsobservations

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Glider 4

Launcher

Rubber band

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Flight path of a glider (120 fps) 6

Parts of the flight path

mg

FA

glidepath

pirouette

mg

FA

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Outline of the report

Air flow around the rotating cylinder

Aerodynamic characteristics of the glider

Computer simulation of gliderComputer simulation of glider’’s motions motion

Explanation of uniqueness of the loop

Typical flight paths

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Air Air flow aroundflow arounda rotating cylindera rotating cylinder

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Flow type behind the glider

4Re 10vr

Flow behind the glideris turbulent

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Aerodynamic force

v

1v

2v

DF

LF

F

Bernoulli's principle: 1 2 1 2v v p p

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Setup #1: wind tunnel

Drive sectionContraction cone

Test chamber

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Wind tunnel scheme

Rotating cylinderPlume of smoke

High speed camera

Prism

Laser

Cylindrical lens

Air turbineElectric motor

Honeycombs

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Cylinder rotates in the test chamber

Electric motor

Cylinder

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Flow without rotation (video) 15

Flow with rotation (video) 16

Induced tip vortices 17

Induced tip vortices

Thouault N. et al. (2012) “Numerical analysis of a rotating cylinder with spanwise discs”.

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TypicalTypicalflight pathsflight paths

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Low initial velocity

Hillshape

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Increasing of the initial velocity

Cuspshape

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High initial velocity

Loopshape

mg

Fa

v

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What is “high” and “low” velocity?

2mg v S

mgvS

3 m/sv

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Zero initial velocity 24

Zero initial velocity (240 fps) 25

Reverse rotation

Arcshape

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Reverse rotation (120 fps) 27

AerodynamicAerodynamiccharacteristicscharacteristics

“Investigate its motion…”

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Aerodynamic forces

Drag force

Lift force

Glider angular velocity

Glider velocity

Depend on

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Spinning ratio

0 10rv

v

r

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Aerodynamic coefficients

212

212

( )

( )D D

L L

F C v S

F C v S

Crosssection

Dynamicpressure

Dragcoefficient

Liftcoefficient

Dragforce

Liftforce

Spinningratio

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The main idea

Wind tunnel?

Glidepath!

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Constancy of the angular velocity 33

Balance of forces on a glidepath

mgv

DF LFcossin

D

L

F mgF mg

F

212

212

( )

( )D D

L L

F C v S

F C v S

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Gliders

А B

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20.02 m12 g; 23 g

Sm

20.01 m5.5 g; 10.5 g; 15.5 gS

m

0

10

20

30

40

50

60

0 2 4 6 8 10

Spinning ratio

Dev

iatio

n an

gle

(°)

А1А2А3B1B2

Vertical deviation angle

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0

1

2

3

4

5

6

0 2 4 6 8 10Spinning ratio

Dra

g co

effic

ient

A1A2A3B1B2

Drag coefficient 37

0

1

2

3

4

5

6

0 2 4 6 8 10Spinning ratio

Lift

coef

ficie

nt

A1A2A3B1B2

Lift coefficient 38

Aerodynamic force

v0

4.5

1

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ComputerComputersimulationsimulation

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Test flight path 41

IP simulation 42

Comparison with experiment 43

Is it possibleIs it possibleto produce moreto produce morethan one loopthan one loop??

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Only one loop!

LF

DF

Radiusr

2

L

mvrF

sStoppingdistance

2

D

mvsF

1 L DF F r s

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Velocity increased 3 times more… 46

SummarySummary

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Main results 48

References

• Swanson W.M. (1961) “The Magnus effect: A summary of investigations to date”. Trans. ASME D83, 461–470.

• Mittal S., Kumar B. (2003) “Flow past a rotating cylinder”. J. Fluid Mech. 476, 303–334.

• Thouault N. et al. (2012) “Numerical analysis of a rotating cylinder with spanwise discs”. AIAA, 50, 271–283.

• Seifert J. (2012) “A review of the Magnus effect in aeronautics”. Progr. Aero. Sci. 55, 17–45.

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