Stearin engine

Nankai University, 2009

A candle is balanced on a horizontal needle placed through it near its centre of mass. When the candle is lit at both ends, it may start to oscillate. Investigate the phenomenon. Maximize the output mechanical power of the system.

Stearin engine

Stearin engine

Stearin engine

α

0 С

N

X

dh

Puncture

Centre of the masses

Origin point

Theoretical explanationTheoretical explanation

φ

d

xarctgA

d

xarctg

2

2

Δx/2

l

ml

m

mx

Stearin engine

Complicated Complicated ExplanationExplanationΔx > 0 when

drops from right end

φ dh

Δx/2

φ

00

00

*2/

*2/

d

tgdxarctgA

d

tgdxarctg

Stearin engine

Puncture near the centre Puncture near the centre of the massesof the masses

Stearin engine

Change of the height of centre of the masses

Puncture point

dropT

hmgP

hmgA

max

Stearin engine

α

Plot combustion speed (Plot combustion speed (ξξ) against ) against angleangle

Stearin engine

Combustion speedCombustion speed

The candle material is the main source of energy

Gazes are mostly burning near the point, where temperature is

maximalWick is in low temperature area,

where it is unable to burn

Under the wick – a puddle of liquid paraffin. The gaze goes

up.

Oxygen for the combustion goes from

bottom upwards

Stearin engine

LevelingStearin engine

Leveling Leveling oscillogrammoscillogrammStearin engine

Plot mass of drop against Plot mass of drop against angleangle

Stearin engine

α

α

α

Oscillations fadeOscillations fadeStearin engine

Oscillations fadeOscillations fade

1

)*(0

17.0

s

eAA TNN

Stearin engine

Computer ModelComputer ModelInput parameters (mass, length, angle, puncture)

Constants (viscosity, combustion speed)

Combustion speed is thought to be random with average value equal to measured

Time is changed for small periods, for each we

recount position of the candle

When the mass on one of the ends reaches critical, it

drops

Stearin engine

Stearin engine

ComparingComparingStearin engine

DropsDropsStearin engine

Period of oscillationsPeriod of oscillations

gd

l

mgd

IT

32

Free oscillation period of a candle:

Stearin engine

ResonanceStearin engine

Stearin engine

Stearin engine

Stearin engine

Stearin engine

Plot Plot ξξ against angle against angle

α

Stearin engine

We’ll suggest, that resonance occurs, when Тfree = Тdrop, and will find conditions, needed for the

resonance.To do this, we’ll find Тdrop:

dropdrop TT

id dttAdtm0

0

0

))sin(25.085.2(

Stearin engine

sml

dm

arctg

gd

lm

TA

Tm

l

d

d

d

250

;8

cos)2(

85.23

;8

)2cos(85.2

0

0

d=0.001 m R=0.003 m

Stearin engine

Stearin engine

Plot Plot ξξ against diameter against diameterStearin engine

Plot V against diameterPlot V against diameterStearin engine

Massive candlesMassive candlesWe will separate a class of massive candles. Massive candles are such ones, which can’t move when one drop falls. It means that the moment of the force is less than moment of frictional forces. Such candle may not oscillate in basic mode, even if punctured at the center of the masses.

Stearin engine

«Scoops»Stearin engine

««ScoopsScoops»»Stearin engine

22

22

12

)*2(3/*

sin2cos

)*2(

*

)(

tgdx

dglN

xdtgd

xdmg

TN

A

T

AP

hhgmА

i

drop

ii

ci

φ dh

Δx/2

φ

Δx > 0 right

Stearin engine

Power in ModelPower in ModelStearin engine

Usage of PowerUsage of Power

2202

~;~~; APA

TRP

Stearin engine

Usage of PowerUsage of PowerStearin engine

Output PowerOutput Power

2

22)

2(

~~

R

mx

l

ddx

arctgAP

Stearin engine

xd 7.0

Stearin engine

Power in resonance modePower in resonance modeStearin engine

Stearin engine is not a heat machineWe need to use candles from paraffin of

about 1sm wide.The resonance effect is the basic of getting

maximal power.The optimal puncture is needed for the

power to be maximal.The best way of using Stearin engine is

transforming its mechanical energy into electromagnetic.

Stearin engine

The effect of oscillations was explainedWe created a computer model, which lets us

imitate effect of the problem We found the parameters, which the

oscillations depend on.We defined optimal parameters for achieving

maximal output mechanical power of the system.

We created a device, transforming the power of oscillation into electromagnetic oscillations.

Stearin engine

Slobodjanuk A. I. “Advance high school physic”

Slobodjanuk A. I. “Computer model of physical processes for high school students”

Y. A. Smorodinsky “Temprature”

Stearin engine

Stearin engine

Стеариновый двигатель

Температура плавления воска находится в пределах от 61 до 65 градусов. При повышении температуры воска на один градус плотность воска уменьшается на 0,0008. При нормальных условиях плотность чистого воска колеблется от 0,96 до 0,98Поверхностное натяжение - парафин 18-28 мН/мПлотность парафина – 0.9МFтр = 1*10-4 Н*м

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