Electromagnetic Coin Flip

1. Electromagnetic Coin Flip Bart Enright Seth Carlton

2. Objectives • Create an electromagnetic cannon to accurately shoot a projectile. • Create a mathematical model that predicts the distance in which the projectile will shoot. • Transfer the force from the projectile to a coin. • Predict the outcome of the coin.

3. Cannon Design Aluminum Cylinder Iron Rod Mount Iron Rod Separator Plastic Piping Inner and Outer Coil Windings

4. 1 I1 2 + I2 I2 V - Cannon Theory The current induces a flux loop through the iron and around the coils Voltage is applied to the coil The voltage creates a current The current in the Aluminum produces a flux which opposes the flux in the iron This creates a current in the Aluminum Cylinder

5. Calculating the Force on the Projectile • Current : I1 = V1/Z, Z = Rwire + jωLcoil V = variable magnitude, angle = 0 Rwire = .7Ω ω = 2π60 L = immeasurable • Magnetic Field : H1 = N1I1 + N2I2 • l lz • N1 = number of turns of coil 1 = 150 • N2 = number of turns of coil 2 = 1 • l = mean length of the flux = immeasurable • z = distance of coil 2 from coil 1 = varying • Magnetic Induction : B1 = μH1 = μrμ0H1 • μr =relative permeability = 150 (for iron) • μ0 = permeability of air = 4π*10^(-7)

6. Calculating the Force on the Projectile • Flux1 : Φ1 = B1A A = cross sectional area of the mean length • Current : I2 = N1d Φ1 • N2 dt • Flux Linkage : λ1 = N1Φ1 , substituting H1 into B1 and B1 into Φ1, • λ1 = μ(N1^2)AI1 + μN1N2AI2 • l lz • Pulling out all the constants into one constant: • k = μAN1N2 , λ1 becomes: • l • λ1 = N1kI1 + kI2 • N2 z

7. Calculating the Force on the Projectile • Solving for λ2 in the same way will yield: λ2 = kI1 + N2I2 z N1 • Co-Energy : Wm’ = ƒ(λ1 + λ2)dI • Wm’ = ½L1I12 + kI1I2 + ½L2I22 • z • Force of Electric Origin : fe = d Wm’ • dz • fe = -kI1I2 • z

8. Calculating the Force on the Projectile • Sum of the forces on the projectile : F = ma ma = -mGsin + fe a = -Gsin + fe/m a = acceleration in the z direction m = mass of projectile = 4oz G = gravitational constant = 32 ft/s2  = launch angle

9. Projectile Simulation • Matlab simulation uses Euler’s integration method to solve the instantaneous-time differential equations representing Faraday’s law ( ) and Newton’s law (F=MA). • The program inputs the Angle and Applied Voltage from the user. • It then terminates when the projectile hits the ground. • The flight path and distance of the projectile are displayed on the screen.

10. Projectile SimulationProgram Block Diagram Initialize variables Input: voltage,angle While projectile distance < cannon length While y axis distance > 0 Calculate forces at time step Calculate force in y direction at time step Calculate new distance at time step, plot Calculate new distances at time step, plot Update variables at new distance

11. Projectile Simulation Matlab Command Prompt » projectile What is the applied voltage to the cannon? 20 What is the angle of the cannon? 60 The distance of the projectile will be 52 inches »

12. Projectile Simulation

13. Flipping Device Frame of Flipping device Coin Nesting Area Piping/Flipping Device Threads Plunger

14. Flipping Device Coin Nesting Area The aluminum ring is projected toward the flipping device The flipping device flips the coin according to Newton’s 2nd law (F=MA)

15. Coin Flip Prediction • The outcome of flipping the coin should be accurate if the same force, voltage and angle are applied each time. • The coin lands in a pool of water with a rag to dampen the landing and increase accuracy. • A database of our experimental results is created to determine the expected outcome. • A program is created in Matlab which accepts the users input for the Angle and Voltage. • The program searches for the probability of occurrence for the applied angle and voltage, then returns the probability.

16. Coin Flip Prediction Matlab Command Prompt » coinflip Enter the angle from 40 to 60 degrees with 5 degree increments. 45 Enter 10, 15, or 20 volts. 15 The experimental odds are 87% heads Place container 20" to 26" from base »

17. Problems & Challenges • The force of the projectile was extremely sensitive to the position of the coils. • The flipping device did not perform to the specifications we had anticipated. • The cannon performed poorly at high voltages because the iron became saturated. • The immeasurable quantities within the projectile program required many trials to determine. • Our switch performed well at first then slowly deteriorated.

18. Recommendations • Use a mold or some other sort of epoxy so the coils do not move. • Use a ball bearing system between the plunger and cap to maintain a constant position and reduce friction • Use a thicker iron bar to raise the saturation level of the iron. • Use a switch that has a higher current rating.

19. Conclusion • The projectile distance was found to be accurate within ¼ inch for voltages under 10 volts and within 1 inch for voltages under 35 volts. • We have a constant force hitting the flipping device. • The coin prediction was accurate at certain angels and voltages. • Our flipping device performed inaccurately when trials were repeated.