Transcript ppt - IYPT Archive

ELECTROMAGNETIC CANNON
Reporter: Hsieh, Tsung-Lin
Taiwan
Question
A solenoid can be used to fire a small ball. A
capacitor is used to energize the solenoid coil. Build
a device with a capacitor charged to a maximum
50V.
Investigate the relevant parameters and maximize
the speed of the ball.
Optimized Situation
Ball
I
1. Magnitizing
t
4. Reverse current
2. Accelerating
3. At middle
5. Accelerating
6. Leaving
Relevant Parameters
I(t)
 Voltage (V)
 Solenoid
 Length
(l)
 Layer
 Radius
(r)
(→Inductance L)
Capacitance (C)
 Resistance (R)
(→frequency)

Ball
Magnetic susceptibility
Resistance
Mass (m)
Shape
Initial position (x0)
1 2
Typical energy
mv
3
2

10
transferring rate: 1
2
CV 2
Experimental Setup
Power supply
Capacitor
Solinoid
A
B
Experimental Procedure
Charge the capacitor five times longer than its time
constant.
 Connect the capacitor to the solenoid.
 Measure the distance the ball flies to estimate the
initial speed.
 Repeat the procedure
above.

Typical Result
Hypothesis
The ball is magnetized.
Moves toward the less magnetic potential.
d
F      B 
dx
d ( B )
1 2
 Fdx   dx dx  2 mv
S
Constant
current
N
F
x
How Fast It Moves
Three time scales:
Magnetic field decay (RLC oscillation)
Magnitization time
Projectile passing through time
d ( B )
1 2
 Fdx   dx dx  2 mv
Simulation Assumptions
Particle.
 Frictionless.


I
Circuit = RLC loop.
 Path is along the axis of the solenoid.

S
Simulation Formulation
l
r
x
d 2x
dB( x )
2 
m 2 

Vdx
1  R 
 R 
dt

I (t ) 
sin
   t  exp  
t
2
2 LC 3 2 2 L   2  2 L
3


2
1
R








L0 nI (t ) 2   l 
l


2
2

r 2Lx    r    x    r  
LC
2
2
2
 


 


Voltage

1
CV 2
2
Speed is positively related to the voltage.
C= 1470μF
 5 layers
 l= 1.5 cm
 Position:
At the entry
 m= 0.014 g

Capacitance

 (t )
I (t )
The optimized capacitance is 1470 μF.
V= 50V
 5 layers
 l= 1.5 cm
 Position:
At the entry
 m= 0.014 g

Numbers of Layers

L(t ), I (t )
The optimized number is 5 layers.
C= 1470μF
 V= 50V
 l: 1.5 cm
 Position:
At the entry
 m: 0.014 g

Position

x (t )
The optimized position is at the entry of
the solenoid.
5
4
3
2
1
Layer
C= 1470μF
 V= 50V
 l: 1.5 cm
 5 layers
 m: 0.014 g

Material

 (t )
As a good ferromagnetic material, iron flies faster
than any other ones.
C= 1470μF
 V= 50V
 l: 1.5 cm
 5 layers
 m: 0.014 g

Fe
Cu
Ni
Co
Summary
Magnetic force→fire the projectile
 Low energy transferring rate.
 Fastest speed: 31.4 m/s

 V=50
V
 C=1470 μF
 Layers=5
 Solenoid Length=1.5 cm
 Position: At the entry
 Ball mass=0.014g
 Material: Iron

Complicated relationship.
Thank you!
Speed vs. Solenoid length
Parameter : Length (1, 1.5, 2, 2.5, 3 cm)
 Initial Condition :

 Voltage:
50 V
 Capacitance: 1470 μF
 Number of Layers: 5 cm
 Position of Cannon: At the entry of the solenoid (0 mm)
 Mass: 0.014 g
Length

The optimized length is 1.5 cm.
Speed vs. Mass
Parameter : Mass (0.014,
 Initial Condition :

 Voltage:
0.083, 0.19 g)
50 V
 Capacitance: 1470 μF
 Number of Layers: 5 cm
 Length: 1.5 cm
 Position of Cannon: At the entry of the solenoid (0 mm)
Mass

Faster when the projectile is lighter.
Sensitivity

Eliminate the data with significant deviation.