lanterns marco bodnár 12.. task paper lanterns float using a candle. design and make a lantern...

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Lanterns Marco Bodnár 12.

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Page 1: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Lanterns

Marco Bodnár

12.

Page 2: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Task• Paper lanterns float using a candle.

Design and make a lantern powered by a single tea-light that takes the shortest time (from lighting the candle) to float up a vertical height of 2.5m. Investigate the influence of the relevant parameters.

Page 3: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Single tea-light

• Mass

5-15g

• Power

40W

Page 4: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

First simplistic model

Power

Losses

Buoyant force

Gravitational force

Page 5: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Is power 40W enough?

• Condition to lift off

SMV

FF gb

Fb – buoyant forceFg – gravitational forceV – volume of

lantern∆ρ – difference in

density of air inside the lantern and outside

M – mass of the candle

σ – surface densityS - surface

Page 6: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Heat balance in lantern

• KA heat transfer constant from 5-25 W/m2K

• S surface of lantern

• ∆T difference of temperatures

• P power of tea light

TSKP A

http://engineeringtoolbox.com/convective-heat-transfer-d 430.html

Page 7: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Ideal gas

RTpM

T

TT

RT

pM

2

Page 8: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Limits of power

T

T

ASK

PT

1)

2)3) SMV

V

SSMTKP A )(

Page 9: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Minimal power to lift off

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

100

200

300

400

500

600

Minimal power

Volume [m3]

Po

we

r [W

]

Page 10: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Limitation of the task says: there is no chance to design such a lantern

Page 11: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Conclusion

• Theoretical calculation of conditions to lift off proved, that tea light doesn’t work…

• Is this the end?

Page 12: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Task ver. 2

• Paper lanterns float using a candle. Design and make a lantern powered by a fuel with constant power that takes the shortest time (from lighting the candle) to float up a vertical height of 2.5m. Investigate the influence of the relevant parameters.

Page 13: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Higher power? No problem…

1500 W

Page 14: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

And it really works...Ready...

Steady...

GO!

Page 15: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Using solid fuel

• Constant power 800W• Lantern can lift off

Page 16: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

How it really works?

• Volume dependence • Time dependence

Page 17: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Apparatus

Lantern

Solid fuel

scales

Solid fuel

Iron for glueing 3 different models – different bottom areas (A)

Page 18: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Model #1: A = 0.06 m2

20 40 60 80 100 120 140 1600

5

10

15

20

25

volume [l]

Lif

ted

ma

ss

[g

]

Page 19: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Model #1: A = 0.06 m2

20 40 60 80 100 120 140 1600

10

20

30

40

50

60

70

80

90

volume [l]

de

lta

Ta

ve

rag

e [

K]

VgTFT

T b

Page 20: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Model #2: A = 0.12 m2

40 60 80 100 120 140 160 180 200 2200

5

10

15

20

25

30

volume [l]

lift

ed

ma

ss

[g

]

Page 21: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Model #2: A = 0.12 m2

40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

volume [l]

de

lta

Ta

ve

rag

e [

K]

VgTFT

T b

Page 22: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Model #3: A = 0.45 m2

150 200 250 300 350 400 450 500 5500

10

20

30

40

50

60

volume [l]

lift

ed

ma

ss

[g

]

Page 23: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Model #3: A = 0.45 m2

150 200 250 300 350 400 450 500 5500

5

10

15

20

25

30

35

40

45

volume [l]

del

ta T

aver

age

[K]

VgTFT

T b

Page 24: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

All models together universal behavior

40 60 80 100 120 140 160 180 200 2200

10

20

30

40

50

60

70

volume [l]

Model #3: A = 0.45 m2

Model #2: A = 0.12 m2

Model #1: A = 0.06 m2

Does the shape matter???

Page 25: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Heat balance

candleBAloss PTKTVKP 3

2

)6(

Heat dissipated through the surface

Heat dissipated through the bottom area

Page 26: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

0 100 200 300 400 500 6000

10

20

30

40

50

60

70

80

90

volume [l]

de

lta

Ta

ve

rag

e [

K]

Theoretical fit

Model #1: A = 0.06 m2

Model #3: A = 0.45 m2

Model #2: A = 0.12 m2

Page 27: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

How it really works?

• Volume dependence • Time dependence?

Page 28: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14

16

time [s]

lift

ed

ma

ss

[g

]

Time dependence (experimental)

Volume 70 l

Page 29: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Dynamic model

dtPdtPdU losscandle

U – inner energy of lantern

Page 30: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Time dependence (exp. vs. theory)

NO FIT! – constants used from previous experiment

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14

16

time [s]

lift

ed

ma

ss

[g

]

Page 31: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

• Volume dependence • Time dependence

How it really works?

Now we know everything we need…

Page 32: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Forces on lantern

Excel simulation

Euler method of finite increments

MS Excel

Theoretical description of motion

Page 33: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

40 60 80 100 120 140 1600

10

20

30

40

50

60

70

80

90

100

volume [l]

tim

e t

o r

ea

ch

2,5

m [

s]

Time to reach 2,5m

Lantern with this volume was produced

Page 34: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Lantern; approximately 75 liters

Page 35: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Conclusion

• Theoretical description of the problem

• With constant power found most suitable volume (around 75 liters)

• But this is not everything…

Page 36: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Task vs. 3

• Paper lanterns float using a candle. Design and make a lantern powered by a modified single tea-light , which doesn’t have to lift on with lantern, that takes the shortest time (from lighting the candle) to float up a vertical height of 2.5m. Investigate the influence of the relevant parameters.

Page 37: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

What changes?

• New relevant parameter• Time of holding

• Small difference in simulation• No extra mass added to lantern• Power dissipates during the flight

Page 38: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Experiment

Highest volume 170 liters

Smallest volume50 liters

Surface density8 g/m2

Page 39: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Time to reach 2,5m

40 60 80 100 120 140 160 1800

20

40

60

80

100

120

140

volume [l]

tim

e to

rea

ch 2

,5m

[s]

Page 40: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Output from simulation

0 50 100 150 200 250 300 3500

20

40

60

80

100

120

140

volume [l]

tim

e t

o r

ea

ch

2,5

m [

s]

Best volume 120 liters

Time of holding 63 sec.

Total time 70 sec.

The fastest one created

Page 41: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

But we found something better

Page 42: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

• The lowest surface density

Highest volume15 l

Lowest volume10 l

Surface density5 g/m2

Second experiment

Page 43: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

10 20 30 40 50 60 70 80 90 100 1109.5

10

10.5

11

11.5

12

12.5

volume [l]

tim

e t

o r

ea

ch

2,5

m [

s]

theory

measurement

Only 1 point, but the best

Not able to lengthen the bag,

because it tears

Bu

rned

bag

Page 44: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

• The lowest surface density

Best volume15 l

Time of holding7 sec.

Time to reach 2,5m10 sec.

Second experiment

Page 45: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Correlation

Page 46: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Conclusion

• Investigated the original task– - No lantern in these conditions can be build

• Modified task to investigate this phenomenon– - Solid fuel instead of tea light– - Modified tea light not a part of lantern

• Found relevant parameters (volume, power, surface, time of holding…)

• Built the quickest lantern for each variant of task

Page 47: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

THANK YOU FOR YOUR ATTENTION

Page 48: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Superlantern 10 sec.

Page 49: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

APPENDICES

Page 50: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Measurement of temperature

thermometer

Hot air going outside has no influence on measurement

Page 51: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Temperatures

Page 52: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Redistributed temperature

•Linear gradient

•Shape approximately spherical

•Outside lantern is 0T

Page 53: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

No manipulation – steady power output

• Power 600W

burning of wax of tea light 4h

of modified tea light 16min

To o tom case horenie ja fajn vediet a pamatat si – ale … nezda sa mi to byt podstatne. Pride mi, ze jedinou podstsatnou informaciou je vykon 600W a ten za samostatnhy slide nestoji.

Page 54: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

First experiment

Highest volume 170 liters

Best volume 110 liters

Time of holding 63 sec.

Total time 70 sec.

Hmm.. Tento slide tiez nie je podstatny. Nestaci to len ukazat a zvyraznit na predoslom grafe?

(navyse, nezda sa mi, ze v predoslom grafe je na 170 L cas 70 sekund :P)

Page 55: Lanterns Marco Bodnár 12.. Task Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time

Forces on lantern

tmc

mcKTPT tt

1

VgT

TF tbt

tavv ttt 11

tvhh ttt 11

mFFFa dgbtt /)(

2

2

1tdt SvCF

Excel simulation

Tieto rovnice su nepodstatne. Staci povedat, ze sme pouzili Eulerovu metodu konecnych inkrementov + Exce a ziskali sme…

Rovnice preloz do appendixu, ak sa na ne niekto spyta. Len si pamataj tie tri sily, ktore posobia na balon