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
1100 F
1650 F
2200 F
3300 F
5500 F
6600 F
7700 F
8800 F
11000 F
Current (A)
30
20
10
0
0.00
0.02
Time (s)
0.04
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
 


 


Speed vs. Voltage
Parameter : Voltage (from 30V ~50V)
 Initial Condition :

 Capacitance:
1470μF
 Number of Layers: 5 layers
 Length: 1.5 cm
 Position of Cannon: At the entry of the solenoid (0 mm)
 Mass: 0.014 g
Voltage

1
CV 2
2
Speed is positively related to the voltage.
Speed vs. Capacitance
Parameter : Capacitance (470μF ~ 3300μF)
 Initial Condition :

 Voltage:
50 V
 Number of Layers: 5 layers
 Length: 1.5 cm
 Position of Cannon: At the entry of the solenoid (0 mm)
 Mass: 0.014 g
Capacitance

I (t )
 (t )
The optimized capacitance is 1470 μF.
Speed vs. Number of Layers
Parameter : Number of layers (4~8 layers)
 Initial Condition :

 Voltage:
50 V
 Capacitance: 1470 μF
 Length: 1.5 cm
 Position of Cannon: At the entry of the solenoid (0 mm)
 Mass: 0.014 g
1.5 cm
1
2
3
4
5
6
7
8
Numbers of Layers

The optimized number is 5 layers.
L(t ), I (t )
Speed vs. Position
Parameter : Position (0~10 mm)
 Initial Condition :

 Voltage:
50 V
 Capacitance: 3700 μF
 Number of Layers: 5 cm
 Length: 1.0 cm
 Mass: 0.083 g
Position

x (t )
The optimized position is at the entry of
the solenoid.
5
4
3
2
1
Layer
Speed vs. Material
Parameter : Material (iron, cobalt, nickel, copper)
 Initial Condition :

 Voltage:
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)
 (t )
Material

As a good ferromagnetic material, iron flies faster
than any other ones.
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!