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 (from lighting the candle) to float up a vertical height of 2.5m. Investigate the influence of the relevant parameters.

Single tea-light

• Mass 5-15g

• Power 40W

First simplistic model

Power

Losses

Buoyant force

Gravitational force

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

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

Ideal gas

RTpM

TTT

RTpM

2

Limits of power

TT

ASKPT

1)

2)3) SMV

VSSMTKP A )(

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]

Pow

er [W

]

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

Conclusion

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

• Is this the end?

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.

Higher power? No problem…

1500 W

And it really works...Ready...

Steady...GO!

Using solid fuel

• Constant power 800W• Lantern can lift off

How it really works?

• Volume dependence • Time dependence

Apparatus

Lantern

Solid fuel

scales

Solid fuel

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

Model #1: A = 0.06 m2

20 40 60 80 100 120 140 1600

5

10

15

20

25

volume [l]

Lifte

d m

ass

[g]

Model #1: A = 0.06 m2

20 40 60 80 100 120 140 1600

102030405060708090

volume [l]

delta

Tav

erag

e [K

]

VgTFTT b

Model #2: A = 0.12 m2

40 60 80 100 120 140 160 180 200 2200

5

10

15

20

25

30

volume [l]

lifte

d m

ass

[g]

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]

delta

Tav

erag

e [K

]

VgTFTT b

Model #3: A = 0.45 m2

150 200 250 300 350 400 450 500 5500

10

20

30

40

50

60

volume [l]

lifte

d m

ass

[g]

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]

delta

Tav

erag

e [K

]

VgTFTT b

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???

Heat balance

candleBAloss PTKTVKP 32

)6(

Heat dissipated through the surface

Heat dissipated through the bottom area

0 100 200 300 400 500 6000

10

20

30

40

50

60

70

80

90

volume [l]

delta

Tav

erag

e [K

] Theoretical fit

Model #1: A = 0.06 m2

Model #3: A = 0.45 m2

Model #2: A = 0.12 m2

How it really works?

• Volume dependence • Time dependence?

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14

16

time [s]

lifte

d m

ass

[g]

Time dependence (experimental)

Volume 70 l

Dynamic model

dtPdtPdU losscandle

U – inner energy of lantern

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]

lifte

d m

ass

[g]

• Volume dependence • Time dependence

How it really works?

Now we know everything we need…

Forces on lantern

Excel simulation

Euler method of finite increments

MS Excel

Theoretical description of motion

40 60 80 100 120 140 1600

10

20

30

40

50

60

70

80

90

100

volume [l]

time

to r

each

2,5

m [s

]Time to reach 2,5m

Lantern with this volume was produced

Lantern; approximately 75 liters

Conclusion

• Theoretical description of the problem

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

• But this is not everything…

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.

What changes?

• New relevant parameter• Time of holding

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

Experiment

Highest volume 170 liters

Smallest volume50 liters

Surface density8 g/m2

Time to reach 2,5m

40 60 80 100 120 140 160 1800

20

40

60

80

100

120

140

volume [l]

time

to re

ach

2,5m

[s]

Output from simulation

0 50 100 150 200 250 300 3500

20

40

60

80

100

120

140

volume [l]

time

to r

each

2,5

m [s

]

Best volume 120 liters

Time of holding 63 sec.

Total time 70 sec.

The fastest one created

But we found something better

• The lowest surface density

Highest volume15 l

Lowest volume10 l

Surface density5 g/m2

Second experiment

10 20 30 40 50 60 70 80 90 100 1109.5

10

10.5

11

11.5

12

12.5

volume [l]

time

to r

each

2,5

m [s

]

theory

measurement

Only 1 point, but the best

Not able to lengthen the bag,

because it tears

Bur

ned

bag

• The lowest surface density

Best volume15 l

Time of holding7 sec.

Time to reach 2,5m10 sec.

Second experiment

Correlation

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

THANK YOU FOR YOUR ATTENTION

Superlantern 10 sec.

APPENDICES

Measurement of temperature

thermometer

Hot air going outside has no influence on measurement

Temperatures

Redistributed temperature

•Linear gradient

•Shape approximately spherical

•Outside lantern is 0T

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.

First experimentHighest 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)

Forces on lantern

tmcmcKTPT t

t

1

VgTTF t

bt

tavv ttt 11

tvhh ttt 11

mFFFa dgbtt /)(

2

21

tdt 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