presented by

Belarusian team

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 explanation

φ

d

xarctgA

d

xarctg

2

2

Δx/2

l

ml

m

mx

Stearin engine

Complicated Explanation

Δx > 0 when

drops from

right end

φ

Δx/2

φ

00

00

*2/

*2/

d

tgdxarctgA

d

tgdxarctg

Stearin engine

Puncture near the centre of 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 (ξ) against angleStearin engine

Combustion speed

The candle material is the main source of energy

Gazes are mostly burning near the point, where temperature is maximal

Wick 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 oscillogrammStearin engine

Plot mass of drop against angle

Stearin engine

α

α

α

Oscillations fadeStearin engine

Oscillations fade

1

)*(

0

17.0

s

eAA TN

N

Stearin engine

Computer ModelInput parameters (mass, length,

angle, puncture)

Constants (viscosity, combustion speed)

Combustion speed is thought to berandom 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

ComparingStearin engine

DropsStearin engine

Period 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 ξ 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

d

marctg

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 ξ against diameterStearin engine

Plot V against diameterStearin engine

Massive 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

«Scoops»Stearin engine

22

22

12

)*2

(3/*

sin2cos

)*2

(

*

)(

tgdx

dglN

xdtgd

xdmg

TN

A

T

AP

hhgmА

i

drop

ii

ci

φ

Δx/2

φ

Δx > 0

right

Stearin engine

Power in ModelStearin engine

Usage of Power

220

2

~;~~;

APATR

P

Stearin engine

Usage of PowerStearin engine

Output Power

2

22

)2

(

~~

R

mx

l

dd

xarctg

AP

Stearin engine

xd 7.0

Stearin engine

Power in resonance modeStearin engine

Stearin engine is not a heat machine

We 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 explained

We 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 0,98

Поверхностное натяжение - парафин 18-28 мН/м

Плотность парафина – 0.9

МFтр = 1*10-4 Н*м

*04.0*50 eR

rRlmgrrNM

R

kk

ml

kl

I

kl

lkdllkldlkVM

fr

л

l l

ires

2

22

33

32/

0

2/

0

2

*

*12

8*322*2

)cos(

cos2/

sin

22

аo

frresо

m

mg

frresmmg

xdmgM

MMMI

mglM

mgdM

MMMMI