1. ELECTROMAGNETIC CANNON Reporter: Hsieh, Tsung-Lin Taiwan

2. 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.

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

4. 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:

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

6. Experimental Setup A B Power supply Solinoid Capacitor

7. Experimental Setup Electro circuits & Capacitors Solenoid & Muzzle

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

9. Experimental Setup (Inductance) 0.5 cm 67 8 9 Layers 0.05 0.10 0.15 0.20 1.0 cm 1 2 3 4 5 678 0.007 0.03 0.06 0.12 0.17 0.34 0.33

10. Experimental Setup (Inductance) 1 2 3 4 5 6 7 8 1.5 cm 0.01 0.04 0.100.140.280.33 0.60 0.63 1 2 3 4 5 6 7 8 2 cm 0.02 0.07 0.150.210.430.49 0.87 1.13

11. Experimental Setup (Inductance) 1 23 4 3 cm 0.45 0.240.110.03 1 2 3 4 2.5 cm 0.02 0.37 0.210.08

12. 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.

13. Typical Result

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

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

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

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

18. l r x Simulation Formulation

19. 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: 0.014 g

20. Voltage  Speed is positively related to the voltage.

21. 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: 0.014 g

22. Capacitance  The optimized capacitance is 1470 μ F.

23. 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: 0.014 g 1 2 3 4 5 6 7 8 1.5 cm

24. Numbers of Layers  The optimized number is 5 layers.

25. 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: 0.083 g

26. Position  The optimized position is at the entry of the solenoid. 5 4 3 2 1 Layer

27. 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) ‏

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

29. 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.

30. Thank you!

31. 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: 0.014 g

32. Length  The optimized length is 1.5 cm.

33. 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) ‏

34. Mass  Faster when the projectile is lighter.

35. Sensitivity  Eliminate the data with significant deviation.

36. 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.

37. Speed Estimation projectile passing time B final