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 1. Magnitizing2. Accelerating3. At middle 4. Reverse current5. Accelerating6. Leaving I t Ball

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 ( x 0 ) Typical energy transferring rate:

Outline  Experimental setup  Experimental procedure  Typical result  Hypothesis  Experimental results and analysis  Summary

Experimental Setup A B Power supply Solinoid Capacitor

Experimental Setup Electro circuits & Capacitors Solenoid & Muzzle

Experimental Setup Solenoids of different lengths and layers Balls of different sizes, mass and shapes

Experimental Setup (Inductance) 0.5 cm Layers cm

Experimental Setup (Inductance) cm cm

Experimental Setup (Inductance) cm cm

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 “steel” ball is magnetized, with the same direction as the magnetic field in the solenoid. SN S

Hypothesis  The ball is magnetized.  Moves toward the less magnetic potential. SN F x Constant current

How Fast It Moves  Three time scales:  Magnetic field decay (RLC oscillation)  Magnitization time  Projectile passing through time

Simulation Assumptions  Particle.  Frictionless.   Circuit = RLC loop.  Path is along the axis of the solenoid. S

l r x Simulation Formulation

Speed vs. Voltage  Parameter : Voltage (from 30V ~50V) ‏  Initial Condition :  Capacitance: 1470 μ F  Number of Layers: 5 layers  Length: 1.5 cm  Position of Cannon: At the entry of the solenoid (0 mm) ‏  Mass: g

Voltage  Speed is positively related to the voltage.

Speed vs. Capacitance  Parameter : Capacitance (470 μ F ~ 3300 μ F) ‏  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: g

Capacitance  The optimized capacitance is 1470 μ F.

Speed vs. Number of Layers  Parameter : Number of layers (4~8 layers) ‏  Initial Condition :  Voltage: 50 V  Capacitance: 1470 μ F  Length: 1.5 cm  Position of Cannon: At the entry of the solenoid (0 mm) ‏  Mass: g cm

Numbers of Layers  The optimized number is 5 layers.

Speed vs. Position  Parameter : Position (0~10 mm) ‏  Initial Condition :  Voltage: 50 V  Capacitance: 3700 μ F  Number of Layers: 5 cm  Length: 1.0 cm  Mass: g

Position  The optimized position is at the entry of the solenoid Layer

Speed vs. Material  Parameter : Material (iron, cobalt, nickel, copper) ‏  Initial Condition :  Voltage: 50 V  Capacitance: 1470 μ F  Number of Layers: 5 cm  Length: 1.5 cm  Position of Cannon: At the entry of the solenoid (0 mm) ‏

Material  As a good ferromagnetic material, iron flies faster than any other ones. Cu Ni Co Fe

Summary  Magnetic force → fire the projectile  Low energy transferring rate.  Fastest speed: 31.4 m/s  V=50 V  C=1470 μ F  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 μ F  Number of Layers: 5 cm  Position of Cannon: At the entry of the solenoid (0 mm) ‏  Mass: g

Length  The optimized length is 1.5 cm.

Speed vs. Mass  Parameter : Mass (0.014,0.083, 0.19 g) ‏  Initial Condition :  Voltage: 50 V  Capacitance: 1470 μ F  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.

Verification  Use a permanent magnet as the projectile.  The projectile won’t affect the LRC oscillation.  Estimate the projectile passing time by a high speed camera.

Speed Estimation projectile passing time B final