Slow descent v3_IYPT

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Q15. SLOW DESCENTInternational Young Physicists Tournament 2011

Republic of Singapore Zhang Nuda

Overview2

From the possible designs, we will pick a best design.

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Content: Chosen design3

That brings us to the 2nd part of my presentation, where I will focus on optimising the chosen design. I will begin with the theory

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Question 15:Design and make a device, using one sheet of A4 80-gram-per-square-metre paper that will take the longest possible time to fall to the ground through a vertical distance of 2.5 m. A small amount of glue may be used.Investigate the influence of various parameters.

4IntroductionTheory: Conservation of energyPossible designs

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Interpretation of question make a device, using one sheet of A4 80 gsm paperMust consume entire paperCan cut into different pieces but entire paper is put together longest possible time to fall to the groundRelease from restNo assisted launch, e.g., throwing, etc5IntroductionTheory: Conservation of energyPossible designs

Released from rest at translational and rotational equilibrium. no net force or torque input.5

Preliminary dataPlain 80gsm A4 paper allow to fallTime to drop 2.5 m approx. 2.40.4 s

A successful device must fall slower than a piece of paper6IntroductionTheory: Conservation of energyPossible designs

Falling paperBack and forth & from side-to-sidei.e. flutteringRotates end over end i.e. tumblingChaotic behavior

(A. Belmonte et al., 1998)7IntroductionTheory: Conservation of energyPossible designs

fluttertumble

Energy consideration: Freefallshortest time to descend H

Uinitial = mgHKEinitial = 0other Einitial = 0Ufinal = 0KEfinal = mgHother Efinal = 08ground

IntroductionTheory: Conservation of energyPossible designs

We approach this question using the law of energy conservation.8

ground

Energy consideration: IDEALUinitial = mgHKEinitial = 0other Einitial = 0Ufinal = 0KEfinal = min.other Efinal = max.Ideally,Min. verticalspeed


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Energy considerationsPossibly convert energy to:Rotational KE Horizontal motion Heat

Introduction of upward forcesLiftDrag


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Possible design: Paper helicopterConcepts:Rotation Drag11


Possible design: Flying wing/gliderConcepts:LiftDragForward velocity12


Possible design: ParachuteConcepts:Drag13


Possible design: TumblewingConceptsRotationForward velocityLiftDragPros:Most modes of dissipationLargest area for drag

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IntroductionTheory: Conservation of energyPossible designsDesigns:Modes of dissipationFlight time:HelicopterRotation, drag2-3secGliderForward motion,Lift, drag1-2 sec

ParachuteDrag2-3secTumblewingForward motion, rotation, lift, dragCapable of > 5sec

15 Initial trials

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Part 2: The Tumblewing16Optimising flight timeIntroductionTheory: maximising dissipationExperimentsConclusion

Now I shall move to the second part of my presentation, where we will focus on optimising the flight time of the tumblewing.A flat piece of paper of any size, when dropped, will either flutter or tumble. Tumbling, occurs when certain conditions of dimensions and orientation are satisfied.(* do demo with card). We can see that when tumbling occurs, the flight time is significantly lengthened. Thus we base our device on the principles of autorotation.16

yxeDesign17leading edgetrailing edgeIntroductionTheory: maximising dissipationExperimentsConclusion

The tumblewing consists of a rectangular sheet of paper. The device has a wingspan y and a chord length x. Aspect ratio AR is defined as y/x, and surface area will be xy. The forward and back ends are folded downwards and upwards respectively to aid in rotation. For simplicity, part folded down will be defined as the leading edge and the part folded up will be defined as the trailing edge (although technically incorrect).

(Q & A: Now you may ask whats the point of the edges. Previously, when the card was flat, it did not tumble when placed flat. By adding the edges, it will tumble when placed at any angle. We are in a sense forcing rotation to occur. And rotation occurs faster with the edges.)

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Flight

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I dont know how to increase play rate. However if I dont have enough time I can cut off the end and put the full video into hidden slides.18

Theory: The Magnus Effect19Lift

Rotation

Translational velocityTraps air; high pressureo

As the tumblewing is released, the leading edge traps air, creating a high pressure region below the leading edge. The resulting torque rotates the card counterclockwise, as it begins to move broadside-on. If inertial forces are large enough, the wing continues past the broadside-on position and the cycle repeats itself. The rotation traps a cylinder of air that rotates with the wing. The wing then moves forward and generates lift through the Magnus effect. Based on the Magnus effect, there will be a driving force that pushes the tumble wing forward. As the wing moves to the left, there is relative airflow to the right. Again, based on the Magnus effect, there will be lift generated.19

Energy conservation20

KE in vertical axisKE in horizontal planeRotational KEDissipation:DragLift FlexingVortex shedding

IntroductionTheory: maximising dissipationExperimentsConclusion

Thus we model the modes of energy dissipation of the tumblewing as such. Energy conversion from potential energy is categorised into the following forms:Kinetic energy in vertical axis, Translational KE in horizontal plane, rotational energy and dissipation through the 4 modes of lift, drag, vortex shedding and flexing.To prolong the descent we want to maximise the modes in green.Now we shall examine which mode of dissipation plays a more significant role.

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Maximise area to increase drag21Drag equationAvg. terminal velocity

Density of air

Surface areaScaling of upward dragIntroductionTheory: maximising dissipationExperimentsConclusion

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Scaling of upward dragMaximise area to increase drag22 Thus we want to maximise surface area


Using the values of velocity and surface area of the tumblewings used in our preliminary trials, we found that work done by drag is on the order of 10-2. Comparing the values with the initial potential energy, we found that drag can constitute over 60% of energy dissipated. Thus, from here we can conclude that the optimum wing must make full use of surface area. This assertion is backed up by experimental results (show in hidden slides)Knowing that we want to make full use of surface area, we now have to find out what shape would give us the maximum flight time for a fixed maximum surface area. Thus, we shall move on to our experimental section, where we will investigate this parameter.22

Experimental designLEGO launcher with quick release cable for consistent unbiased releaseConducted in enclosed room without winds23


We built a LEGO launcher with a quick release mechanism to eliminate any possible human error from launching by hand. The launcher allowed us to vary the launch angle of the wing. The experiment was conducted in an enclosed environment to eliminate wind. All descents are captured on high speed camera for video analysis. Only data in which the wing had reached steady state was analysed.23

[1] Effect of aspect ratioIndependent variable: Aspect ratio y/x

Dependent variableFlight timeConstants:Area, xy (4503)cm2Edge width (1.000.05)cmMass (4.9900.005)gLaunch angle (45.00. 5)deg

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x

y3.04.14.55.06.28.010.011.011.712.112.913.914.916.017.2


In our first experiment, to find the optimum aspect ratio for a fixed surface area, we built 15 tumblewings with AR varying from 3.0 17.2. A surface area of 450 was chosen because it was close to the maximum surface area of the paper and it allowed for easy variation of wing dimensions. We also fixed the edge width at 1cm and the launch angle was fixed at 45.

If they say the flight time some high some low is because your surface area is +-3, say that we measured the surface area for each wing and that those with shortest flight time were not the ones with the least surface area. Thus such a small variation in SA had little influence on experimental results.24

[1] Effect of aspect ratio25

Optimum AR = 4.5 (45x10cm)


Here is a graph of flight time against aspect ratio. We can see that there is no clear trend between flight time and aspect ratio due to multiple modes of dissipation present and complex interactions of the wing with air. However, we can see that optimum flight time is achieved with a wing of AR 4.5. Thus we have determined the optimum aspect ratio for a fixed surface area.25

Variable: edge width, e0.3 0.6 0.9 1.0 1.2 1.5 1.8 2.1cmConstants:Span, y (45.000.05)cmChord, x (10.000.05)cmLaunch angle (45.00. 5)degAssumption:Change in mass will not affect flight time

[2] Effect of edge width26e

x

yIntroductionTheory: maximising dissipationExperimentsConclusion

Next, we thought that edge width might affect flight time as well. Thus, for experiment 2, using the best wing from the previous experiment, we varied the edge width, with launch angle fixed again at 45deg.26

[2] Effect of edge width27

Edge width as small as possible


Here we can see that flight time decreases with increasing edge width. Thus we can conclude that we want to have as narrow an edge width as possible.27

[3] Effect of launch angleVariable: Launch angle 0 120deg, at 10deg intervalsDependent variable: timeConstants:Span, y (45.000.05)cmChord, x (10.000.05)cmEdge width (1.000.05)cm

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Direction of flightIntroductionTheory: maximising dissipationExperimentsConclusion

Next, we thought that launch angle could have an effect on descent time as it can influence how long it take for the wing to transition into rotation. Thus in our last experiment we varied the launch angle , where the angle from vertical. We used the same wing from previous experiments, with AR 4.5 and edge width 1cm.28

[3] Effect of launch angle29IntroductionTheory: maximising dissipationExperimentsConclusion

DeadZoneModerate launch angle

In the graph of flight time against launch angle, we found that launch angle only affects flight at 0 or past 70deg. Within this range, launch angle will not affect flight time. At 90deg, fluttering occurs at launching. Past 90deg, is the dead zone, where the wing slips backwards, and the motion becomes chaotic. Here we conclude that we want a moderate launch angle.29

[4] The best tumblewingCharacteristics:AR of 4.5Maximum surface areaSmall edge widthModerate launch angleOptimum model:

30Span/cmChord/cmARSA/cm2Edge/cm48.611.84.1573.50.5


In conclusion, we found that the best tumblewing must have the following characteristics. With this knowledge, we designed our optimum model.30

[4] The best tumblewing31


Comparing the flight time of our optimum tumblewing, shown by the orange bar, it clearly has a much longer flight time than all other tumblewings tested.31

ConclusionDevice with longest flight time: TumblewingRotationForward velocityLiftDragMakes maximum use of drag as entire area of paper is exposed.32Makes use of most modes of dissipationIntroductionTheory: maximising dissipationExperimentsConclusion

ConclusionFlight time determined by:Surface areaThe larger the betterAspect ratioBest AR = 4.5Edge widthAs small as possibleLaunch angleModerate angle between 10-60deg

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Thank you34

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Possible designs

Concepts: (1) Rotation (2) dragProStable due to rotation

ConHard to scale to A4Long wingspan - flimsy

Paper helicopter38

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Possible designsConcepts: (1) Lift (2) drag (3) forward velocity

ProLarge surface area for drag & liftDihedral wings can ensure stabilityConStall state when dropped from rest

Flying wing/glider39

12. A glider needs to be given an initial forward velocity to generate the lift to fly. If dropped from rest, it is initially in a state of stall, and has to dive to gain enough airflow over the wings for lift. This initial dive sacrifices too much flight time for a glider to be effective.39

Possible designsConcepts: (1) drag ProMaximum use of dragConPaper parachute is top heavy flips over

parachute40

Concepts: (1) Rotation (2) forward velocity (3) Lift (4) Drag

Possible designsProMost modes of dissipationLarge area for dragConVery flimsy

tumblewing41

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Expt. details: helicopterApprox. 70% of paper as bladesVaried angle of attack and measure flight timeTiming increases over falling paper by 10 20%

Angle of attack / oTime in air / s02.30 0.1372.71 0.13102.91 0.13152.85 0.13202.81 0.13

Expt. details: glider15 models of paper gliders with initial launching angles 0, 20, 40, 60 and 80. Bank and pitch corrections made via ailerons and elevators.

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Flight times barely exceed 2sec

Expt. details: parachute44

Parachute Avg time: 2.28sBlunt head Avg time: 2.58s

Measurements & calculations45IntroductionTheory: maximising dissipationExperimentsConclusion

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Launcher

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VorticityKrmn vortex street (R. Mittal et al., 2003)Periodic vortex sheddingStrength and frequency of vortex shedding and rotation rate interacts in complex and unknown manners.

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Flow visualisation48

Aluminium plate in water (1.2 x 6cm)Re ~800Shedding frequency = 4t=0t=0.5t=1.0t=1.5

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Theory: High pressure49Done with Solidworks Fluid AnalysisLiterature: Tumbling cards, L. Mahadevan et al., 1999Unsteady aerodynamics of fluttering and tumbling plates, Z. Jane Wang et al., 2005

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Magnus effect50

32. This shows that as rotation rate increases, horizontal velocity increases, proving that the Magnus effect exists.50

Magnus effect51

Magnus effect52

Magnus effect (theory)53

Drag equation applied to tumblewing54

Scaling of upward drag

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Drag equation applied to tumblewing55

Effect of surface area56

36. Combining the results of the previous 2 experiments, we can see that it is surface area, and not shape, that has the most significant effect on descent time. 56

Predicting flight time57

Comparing skin & form drag58

Small edge width indeed betterFor the optimum tumblewing 2 models were actually tested.

59Edge widthARFlight time1.0 cm4.55.546 0.0080.5 cm4.16.049 0.008

General behaviour of tumblewing60Tumbling Cards, L. Mahadevan et al., 1999

61General behaviour of tumblewing

Properties of A4 paperPropertyValuesMass:4.990 x 10-3 kgDimensions:0.211m by 0.298 m (0.0629m2)Volume: 6.917 x 10-6 m2Density730 kgm-3

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Data sheet63

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Slow descent v3_IYPT

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