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 t 1. Magnitizing 2. Accelerating 3. At middle 4. Reverse current 5. Accelerating 6. Leaving

Relevant Parameters I(t) Ball Voltage (V) Solenoid Capacitance (C) Length (l) Layer Radius (r) (→Inductance L) Capacitance (C) Resistance (R) (→frequency)‏ Ball Magnetic susceptibility Resistance Mass (m) Shape Initial position (x0) Typical energy transferring rate:

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. S N Magnetic domain model Loop model Constant current F x

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

Simulation Formulation x

Voltage Speed is positively related to the voltage. C= 1470μF 5 layers l= 1.5 cm Position: At the entry m= 0.014 g

Capacitance 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 The optimized number is 5 layers. C= 1470μF V= 50V l: 1.5 cm Position: At the entry m: 0.014 g

Position The optimized position is at the entry of the solenoid. C= 1470μF V= 50V l: 1.5 cm 5 layers m: 0.014 g 5 4 3 2 1 Layer

Material 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 Co Ni Cu

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, 0.083, 0.19 g)‏ 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)‏

Mass Faster when the projectile is lighter.

Sensitivity Eliminate the data with significant deviation.