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